Pros
Exciting Missions, lots of opportunity. Gives you a sense of pride in contributing to the Nation's Space Program. Lots of portability around the Agency and federal Government jobs as a whole. The legacy of awesome is everywhere! Meet astronauts, legends, and see cool mission hardware. Great work/life balance. You're not expected to respond to email or answer your phone after work hours. If you work or travel for work outside of work hours, you're compensated appropriately for the time. Training is thorough, comprehensive, and helpful. Very defined career paths, and lots of movement is available.
Cons
Your pay is at the center of public attention and on the news all the time. Low pay compared to private sector (GS Payscale), and it is in the cross-hairs for cuts all the time. Bureaucratic at times, especially at HQ level. No free food or massages like other silicone valley jobs. Can't cut the dead weight because no one gets fired. (This is a pro if you're lazy)