Lots of opportunities, great benefits, at the cost of a slow pace
Pros
NASA is consistently rated as one of the best places to work in the federal government and I believe that's reflective of the high amount of pride that comes with the work. NASA has a large breadth of work from aeronautics, to science, to human spaceflight, which translates to lots of opportunities. Over the course of 15 years I managed to work on multiple projects/programs and even temporarily transfer to another NASA center (Headquarters). As with all government positions, the benefits are good. You receive plenty of leave (depends on seniority but eventually I earned 8 hours of paid leave every 2 weeks), there's an increasing amount of flexible schedule (9/80) work, telework, separate sick leave, government 401k (TSP) with matching, federal health benefits (FEHB), etc. There's also a heavy interest in work-life balance. If a family or home issue came up, I would be able to simply send a note to my supervisor or catch them in the hall and mention the times I'd be out. This flexibility comes with trust in the employees which certainly grows as you prove your dedication to getting the needed work done. In summary, NASA is a good place to work with many friendly and passionate people, good benefits, and interesting work in comfortable environment.
Cons
Most all aerospace projects take time (many years/decades) to go from conception to implementation. NASA is not exempt and has the added complication of facing constantly changing political winds every 4-8 years which directly affects the agency's priorities. Some areas (such as aeronautics) see a little less shift while others (predominantly human spaceflight) can experience major programmatic changes each political cycle. This means you typically have the choice of working large scale programs that move at a snails pace or on new, innovative projects with a very high likelihood of cancellation or outsourcing, leaving you with little sense of fulfillment. If you're an experienced aerospace veteran, you may have grown numb to this and find NASA's benefits outweighs the potential lack of fulfillment. However, younger employees will (and have) grow(n) frustrated and leave. You could find yourself working 10+ years on an exciting project to only have it massively restructured. While I started as a student employee, I would highly encourage young engineers to first consider work at some of the more innovative, faster-paced startups in aerospace to gain experience unless your desire is simply career stability and being able to say "I work at NASA." Similarly, while hands-on engineering work does occur at NASA, those projects are at higher risk of cancellation as the work eventually transitions to a contractor and you're left to supervising a contract and engineering progress. Fine for an experienced engineer wanting exciting but easy work, not so engaging for a young engineer looking to exercise their creativity. I caveat these cons with the fact that NASA is a big organization. Each center has its own unique culture where some take greater pride and effort in rapid, innovative development while others wish to maintain more of a slow and steady pace of development despite constantly changing priorities. Do your homework and reach out to employees at the center your interested in to see if you'd really find the work engaging or if you're merely drawn to it because "its NASA."