Pros
Fantastic travel opportunities and neverending challenges. Responsibility and leadership training fast and early. You truly get out of it what you put into it, including educational opportunities and advancement. Promotions are based in great part on merit, but you need to understand what blocks you need to fill in order to make it and also be able to test well in order to score high enough on the promotion tests. If you get your CCAF (associate degree from the Air Force) in Paralegal Studies, it is accredited by the American Bar Association.
Cons
There is never enough money or manpower to truly get the job done right, and there never will be. You will often have to work long hours and should expect the work to be thankless. As a paralegal you are doing the drudge work that the attorneys don't want to do, and even once you move up in rank you're still going to be doing the same work you did as a junior ranking person - it will just be the more complicated stuff. It's not a stepping stone to becoming a lawyer and the work is not quite the same as paralegal work in the civilian world.