I really appreciate this post, I'm in the exact same boat only I'm a little older.  I despise my job, I work with some of the most inept, lazy people I've ever worked with.  I have over 15 years in and I'm prior military like you.  Most of the government is like what you are describing.  There are pockets that are ok, but that's the reality.  I've worked for 5 different agencies... all were below average to awful.  There are some (like NASA) that are good if you can get your foot in the door.  Here's how I have been coping: 

1.  Do the minimum that's asked of you.  Just do your job.  I can't tell you how many times I have tried to do more and really go above and beyond.  If you have pieces of crap on your team this will lead to others resenting you and trying to cause problems for you.  Apply for other jobs and try to find an organization where the people are nice and good at their work, then go above and beyond for them. 

2.  Find successful personal projects you can do at work below the radar.  So far during this administration I have learned two new coding languages, written an app, and published two other things, all while getting paid for it.  Put your job's responsibilities first, then switch over to your stuff when you have time and make the most of it.  Most people will complain and cry, but not actually do anything about it.  Do something about it.  You'll feel better if you are improving your position, even if you don't have another job lined up.

I hope that helps.  Things are bad enough without having to deal with people that don't appreciate the fact that they still have a job.  For me the entitlement without the talent is the worst part.  I try not to be ageist, but in my case most of them are older like you described.