Now. Here's what you need to acquire proficiency in through your 4-year bs

So I have written this like the advice I would give myself if I could travel back in time or what I really hope to see in the undergrads I want to hire. I hope you don't get discouraged/put off.
First thing: Solidworks/ProE/AutoCAD/Rhino/Blender/CATIA and GD&T are not skills for degree'd engineers. You don't do a BS/ME for draftsmanship. It's like putting MS Office on your resume. You can pick that skill up on your own time.
Second thing: I am talking about becoming an engineer here. You know, the kind that build rockets and microengines (Sandia MEMS Home Page). I have nothing against grades, but I don't care very much for them. So I am not talking about getting the best grades.
Now. Here's what you need to acquire proficiency in through your 4-year BS.
0. Read Wikipedia.
1. Programming - Start with Matlab/Python. Then graduate to C++. An example of a programming goal would be to use this to create your own computational graphics engines. Why? Because this teaches you about visualizing vectors, arrays, transforms and leads you to higher-dimensional algebra. Make sure you can understand and implement Runge-Kutta family of algorithms before you think you are done. A recommendation would be to ditch Windows and move to some flavour of Linux or Mac. You need to understand concepts behind batch/shell scripting and importing open source scripts to embed inside your own. If you don't do anything else in your freshman or sophomore years, that's fine. But make sure you master this.
2. Linear algebra and differential equations - Now, most ME syllabi force the courses on you early on. But very few MEs truly understand these topics. This is the source of all ME theory. I CANNOT STRESS THIS ENOUGH! Most ME professors DO NOT understand linear algebra or its importance - they will fuck it up for you so you will be confused/avoid derivative topics forever. Don't take these courses offered inside your department - take them from CS or EE or Math professors. Or learn it from Gilbert Strang on Youtube. Tie this together with your programming to create numerical simulations. Do NOT take these courses until you are done with your programming.
3. Statistics - Take this twice. Audit it as a freshman. Then take the course again as a senior. This will be the single most important course you ever take as a professional in any field.
4. Engineering mathematics -The rest of your life depends on this. Pay attention to spatial transforms, Fourier analysis, Complex analysis, Potential theory, PDEs, Interpolation/curve fitting, optimization theory. Look for ways to implement these concepts using your programming skills. If you ever wonder about the usefulness of any of this, or you get the choice to skip a few topics - you are doing it wrong. Good engineers use these concepts EVERYDAY.
5. Dynamics/Advanced dynamics - Take this in the Physics department. ME profs screw it up here again, they focus on the mechanics of algebraic manipulation and don't explain concepts very well. Your objective would be to be able to independently construct FBDs of complex interacting mechanisms, and generate classical non/autonomous, non/linear differential equations that describe the time-history of the system. Develop a familiarity with index notation and tensors and operator spaces. Your indicial programming experience will really help you here.
6. Statics/Solid mechanics - Master Timoshenko Goodier/Theory of elasticity. Even if it takes you the rest of your life. If you got through point 2, you should be able to point out the inefficiency of the SFDs and BMDs and Mohr's circle concepts. Try visualizing the simple cases while cognizant that life is not simple. Use your programming finesse to program numerical solutions to your ODEs and equations.
7. Vibration theory - If you actually got through point 2, you will find this a breeze. All they do here is study a second order, non/homogenous, non/autonomous non/dimensionalized ordinary differential equation and the effects of parametric variations (mkc, forcing frequency). If you got through 5, you should be able to figure out all the base excitation, seismic perturbation, isolation, rotating machinery concepts. If you got through 6, then plates/beam vibration problems. If you got through 2 & 4, you will be able to work through MDOF systems and all the modal analysis techniques. This is where you segue to coupled SHO/QHO concepts.
8. Thermodynamics/Fluidics - I am not the right person to advise on these topics. But they are pretty straightforward at the undergraduate level and mostly applications of differential equations and continuum mechanics.
If you followed instructions so far, everything else is a straightforward application of what you should have learned by now. That's all you really need to be a degree'd mechanical engineer - math and physics. Everything else is a specialization and extension of domains from the presented fields into specific tasks. This is also where you start encountering professional jargon. And don't let terms/eponyms scare you off.
Also mechanical engineers don’t generally design machines from scratch – hobbyists and mathematicians do. We follow standards for our industry, mix and match components, or use well defined algorithms to create a new one. There are concepts in kinematic chains, algebraic linkage synthesis and design that are used here. So sure you can read about gears and machinery and 4-bar linkages and cams and geneva wheels, but it is highly improbable that you, as an ME, will create one. It is more likely that a technician or a sheet metal worker will create something utterly brilliant. So if that’s what you want to do, figure on grad school. You can however use your solid mechanics skills to design the components to withstand pyrotechnic impacts.
I skip over manufacturing and 'product engineering' classes because they are shit, when taught in school. You can't master manufacturing sitting in a class, and you certainly are never going to learn enough in school about how to design a full product. Those axiomatic design principles and synectics and product lifecycle management and ideation and Gantt charts and brainstorming processes are bullshit. Nobody in real life does that. Those who do, are not engineers. If you really want to understand manufacturing, skim through Manufacturing Processes for Design Professionals by Rob Thompson, then go talk with people on shop floors, or watch how it's made on Youtube. If you really want to understand the product design process, follow Kickstarter h/w startup stories.
Do not ever waste your time on survey or presentation courses. Avoid attending school seminars if you are not interested in the topic. You should attend all seminars that promise to show you math or process or cool videos. You want to keep an ear out for examples and case studies that show explicit details of how systems get modeled/implemented using math or experiments. Avoid 'design' seminars (usually a peddler from Wharton or Sloan or Kellog) - they are pretty, but pointless.
Take all lab classes you can. ALL of them. All you can afford. Pottery too, if you have that option. Just drop in to watch other people work if you got the free time. Pottery as well. Use the equipment there till you break it - You are paying for it anyway. Make all the mistakes you can ever imagine there. AND DON'T FUCK AROUND IN THE MACHINE SHOP BRO!!!
Amongst other advice, find a PhD student about to graduate every year and get them to mentor you. Don’t believe in that ‘I am busy’ crap – they all are usually on Quora or editing Wikipedia anyway. I speak from experience. Pick people from diverse fields – machine learning, operations optimization, public policy, neurobiology, kernel development … You want to understand what they do, how they do it, what they use to do it and create a possible job network. You don’t want seniors to mentor you because, unless they go to grad school, they will never be in any position to introduce you to great opportunities on time scales relevant to your interests.
Now, let's talk about being a professional mechanical engineer
9. Read ISO/ASME/ASTM/ASTC/ASMI (standards organizations) standard practices. That's the only place where they really tell you how theory meets practice. If you believe your university doesn't provide you access to those - Sue them! Beg/borrow/steal. Whatever. But if you really want to know how things are done; Read the standards. Not the website and their discussion forums. Read the standards.
10. Take/Audit courses on electromagnetism, digital electronics, electrical theory, VLSI/Silicon based designs, electrical machinery. You should be able to design your own motor driver/filter/power regulator/multivibrator circuits and implement them on PCBs. Start dipping into embedded microcontrollers here. This is where you C++ experience should start paying off.
11. Signal processing - Audio/image/Power signals - Master the topic of discrete Fourier transforms/spectral densities and how they are used and calculated. Figure out how digital sampling and digital filters work and how filters and masks get designed. Move on to z-transforms and recursive filters. Your statistics background starts to become useful here. At least figure out how to manipulate images using pixel-array math.
12. Control systems - THIS ties up everything. And THIS was the topic that really got you into ME. You didn't join ME to make bridges or prepare CAD layouts for GE ovens or tractor engines or boiler chambers for plants or be a grease monkey. You joined ME to make structures that move, intelligently. If you have done things right so far, this is where you will get to have fun. It ties together your dynamics and linear algebra first, then programming, signal processing and statistics next, finally you implement it all using your electronics/embedded skills.
13. Instrumentation – People have equipment that costs between a thousand dollars to over several million. You need to learn how to use them, AND how to construct them. You will find that making equipment is always cheaper than buying a turnkey system from a manufacturer. So companies prefer to design/assemble their own systems. This should segue into design of experiments/statistical validation. Your goal should be to know how to hook up the hydraulic pressure gauge in an EMD F51PHI locomotive cab suspended 10 ft up in a shed to an office in Minnesota.
Along with instrumentation, you will frequently need to develop software to control the instruments. Some people use labview, but with your mastery of C/matlab you will do better.
If you want to get into finite elements, you can’t do that in undergrad. All you will learn is to push buttons. Most engineers only think they understand FEA – they actually don’t. It takes practice, study and experience. The pretty pictures don’t mean much by themselves. So I will say go to grad school or intern with a practicing consultant.
That should about cover your basics and get you a good job. But if you want to get a great job, you will need professional degrees or exhibit skills in some of the following. So, on to specialization:
1. Fracture/fatigue/materials on the nanoscale.
2. MEMS – Look up Sandia National Labs/MEMS. Biggest opportunity for MEs since all companies are moving from RnD to ramping up production right about now. Micromachining and processing technologies research is active as well. MOEMS was hot, sensors are sizzling, actuators not so much, lab-on-chip was meandering about, last I checked. Significant effort underway on determining lifetime/reliability as well. People were excited about energy harvesting, but that seems to be toned down now. Lot’s of material science opportunities.
3. Microfluidics – These guys blow bubbles through microchannels! Look up lab-on-a-chip.
4. Bioengineering – Tissue printing/engineering! There’s also research on mechanical characterization of bio-materials (bones/ligaments/RBCs)
5. Medical devices/robotics – da Vinci/intuitive. Also swallowable robots and cameras. Lots of health monitoring devices and OR assistants.
6. Robotics/control systems – Typically, you need to be core CS/EE for this. They are the ones doing most of this research. But you can create opportunities for yourself by choosing to focus on dynamic structure design or kinematics or something on that order. Look up Hod Lipson/Cornell or Red Whittaker/CMU or Marc Raibert/ex CMU/MIT leg labs or Rob Wood/Harvard for inspiration. Google and Amazon have raised this field’s profile over the last couple of years. Look up compliant mechanisms/robots, autonomous vehicles, haptics, telepresence, Raytheon XOS II,... Lot’s of bullshit in the name of ‘assistive robotics’ (that no one can or will want to afford or use, and medicare won’t support).
7. Control systems/avionics – I worked on optimizing damage-resilient, real-time coolant distribution through nuclear subs, my ex-boss worked on guidance systems for the Pershing/Hera systems. This is a mature engineering field at the moment (not much RnD) but scope for new applications.
8. Thermo research – They do crazy things with combustion, not my domain.
9. Nonlinear dynamics – Applied theory, predicting weather(?!), galloping (hopf) systems, .. this field goes on till quantum cryptography and then some.
10. Aerospace vehicles – SpaceX. Etc. Vibrations theory, dynamical systems and controls. Your vibrations theory needs to be strongly coupled.
11. Infrastructure – Given Keystone or fracking, infrastructure is going to undergo another massive boom.
12. Petroleum - …
13. FEA – Meshing and geometry algorithms, data compression, rendering are being researched
14. Energy – fuel cell research, the cryptozoology equivalent in ME They’ve been at it for a while, but it seems to be a funding generation ploy.
15. Marine systems - …
16. Theoretical systems – Lots of work on rule based machine learning based design synthesis, structural optimization (back in early 2000’s it was all about simulated annealing and genetic algos, now they call it machine learning), dynamic self modeling, multi-agent systems,
17. MAV/Flight dynamics – Concentrated around rotorcraft/flapping wing architectures. Mostly experimental, some theoretical research going on.
18. ICE research – Very avoid!
19. Tribology - Nonlinear dynamics of rate state dependent friction generate P/S/Love/Rayleigh wave phenomena used to predict earthquakes. Studying hydrodynamic lubrication of journal bearings is a trifle boring compared to that. See Ruina's work at Brown.
Universities on the West and East coast typically work on the new frontiers of research, while the rest work on last-century concepts. So if you go to school in AK, you will find stuff on corrosion, rotor blades, missiles, defense, aerospace machining … But if you are in MA, you will find machine learning, robotics, vision, SLAM, MEMS, materials, algorithmic synthesis, complex systems etc.
I have written this like the "Survival guide for mechanical engineers on the journey to create astonishing engineering". This is written with North-American ADHD undergrads in mind. So I tend to be didactic, and, in the spirit of times, use hyperbole to signify importance (no selfies, however. Much disappoint.). I also abuse education professionals profusely - But that's only my personal experience – all the additional work I had to put in because courses were not designed right, or because a newly hired asst professor was in charge of a particular course that they had no experience in or because the lecturer, originally from Asia, had this distracting accent and circuitous description that just beat about the bush more than I could keep track of or maybe because most of the freshman/sophomore/introductory courses, specially non-core ME courses, are generally fanned out to temp staff/lecturers that generally don't know jackshit about how things are done or don’t care. So you see, personal failing on my part. That's my excuse for the abuse. And there's catharsis involved as well. So I apologize in advance.
I have a BS/AME USC, and MS/MAE, UC system, PhD/ME (and RI+LTI+ECE) CMU. I wasn't a great student during my BS; 2.7 GPA, almost dropped out to be a professional musician. GRE 1600/6.0 happened. I joined the master’s program because I was getting a fellowship & stipend. Programming happened. YouTube happened. OCW video content happened. I worked on projects with all or some of the following labs - LLNL/SNL/LL MIT/NRLMRY/NECSI/SFI through my PhD. For your reference: MS/PhD GPA 3.6/3.8. No money, at the time of graduation. Now making some.