Pros
Okay. I had to dig deep to come up with this one: you can put on your imagination cap and tell yourself you're a super spy and can't tell anyone anything about anything. The stress and misery of the work is just making you mentally tough, like training to resist torture or something. It's obviously not true and is only fun for like 4-5 minutes tops, but I had to write something here.
Cons
Toxic leadership rules by fear and ridicule. They will leap at every opportunity to rub every single mistake in your face to publicly humiliate you in front of the entire office. If you ever ask any questions, you will be told off or sent a "Let Me Google That For You" link. If you do your work without gathering requirements because they were too important to answer questions and Googling "what does my boss want this application to do" as suggested didn't get you those answers, they're literally mad, and I'm quoting verbatim here, that you didn't "read their minds". If you don't do your work because you're waiting on requirements, well then you should be fired for not doing it.
There's a derogatory stereotype that "government employees can't be fired," which is not true, and they will threaten you with firing for everything: leaving for a doctor's appointment that you scheduled weeks in advance, getting sick and calling in, getting sick and coming in anyway, going to the bathroom, breathing the wrong way, and so on. Then after all that time being told you deserve to be fired, you quit, and they bemoan how inconvenient it is that you're quitting and how hard filling positions is.
The work isn't anything special, either. You may be convinced through official publications or some of NSA's open-source tools or other sources that this is going to be really awesome high-tech stuff. It's not. It's the same boring IT work you could find anywhere else for much better pay and far less organizational dysfunction.
The veneer of secrecy is less "we can't tell you what we work on" and more "if you know what this job is going to be, you would never accept it." For my position, I was flown out for processing and for the interview, and the interviewers didn't even show up! Add several layers of bureaucratic red tape, severely outdated technology, and it becomes even more unpleasant. If you are in processing to work here and you can land a job literally anywhere else, go with that instead. Your mental and physical health will thank you.