1. Is there anything you can do while in the Navy to make yourself a better applicant?
2. Did you ever have time to take some extra classes at a local college?
3. How did you have time to study for the MCAT...or apply to med school for that matter...I hear the life of a nuke is pretty busy?
Necro - I'll see if I can add anything to the previous answer (I'm a Nuke SWO who punched out in Nov 2006; since then, I've managed to keep far, far away from civilian power generation.) I'm studying for retaking the MCAT (took it in 2000 - expired) and planning on submitting apps in June 2010.
1. Been asked this many times, honestly the best thing you can do regardless of what you want to do after the military is to be **** hot. Be a good officer for your sailors and chiefs. Your department head will appreciate this and your fitreps and letters of recommendation will reflect it. Keep in touch with your old dept heads and CO's when you or they move on. You honestly won't have much time to voluteer in the capacity that would sway an adcom's decision.
2. Best option, again regardless of what you want to do after, is to take advantage of the special deal Master's programs that are offered to nuke officers, i.e. Masters of Engineering Management from Old Dominion University. Virtual classes, take tests on the ship. You get a ton of credit for the nuclear training pipeline course work you do in Charleston. It's a good deal, if a bit of a pain in the ass sometimes. You will have other people on the ship doing the same thing, which makes it more tolerable. As mentioned previously, doing anything else while in Chareston for power school and, especially, prototype is not possible. It is a dark, time-sucking rabbit hole that you slip into and come out the other side wondering where the last 12 months went and why you have memorized every valve, pump and control system for a power plant used nowhere else in the world. It is a special experience, that like med school apparently, can only be understood by those who live through it.
3. This one depends on many, many variables. I wasn't studying for the MCAT or applying while still in, but I did do the ODU Master's program. The best thing that could happen for you to be able to study for the MCAT in the Navy is to go on deployment. Did three on two different ships, and the amount of down time is sometimes stunning. Even with a terrible watch rotation, you can still have more time to study in a day than you can probably stomach. Conversely, you can become a god at any number of video games. Deployment is an exercise in repetition. Make a schedule that works for your watch rotation, it can easily be done. I should also highlight that this is dependent, again, on you being a good officer. If you work hard and qualify for your assigned watchstations quickly, you get left alone and have free time to study or get really really good at Halo. If you aren't, you get ridden pretty hard and you spend your free time working on qualifying.
Hope this helps, if you have any other questions feel free to PM me at any time.
Best of luck,
Jeremy