Pros
Engineers at SpaceX are given an unprecedented level of individual responsibility and control over critical hardware from Day 1. The company is constantly pushing boundaries and generating press that makes the employees proud to tell their friends and family they work at SpaceX. There is somewhat less internal politics than other companies, mainly because there is so much work to do that you generally end up fighting to NOT do something, rather than fighting to bring more work in and grow your domain. The company has been growing very quickly which leads to promotion opportunities and has made the stock very valuable. Not guaranteed to continue though.
Cons
Working at SpaceX takes over your life. It is hard to find time and energy for any other significant commitments outside of work, whether they are family, exercise, or hobbies. If you are married, and your spouse does not work at SpaceX, they will grow to hate SpaceX. For the amount of responsibility and stress you have, the pay is not great, unless you end up being able to benefit from sale of stock options. On the other hand, for the number of years experience you have, the pay is generally competitive. There are a lot of employees at SpaceX who have never worked anywhere else. Sometimes it seems like an overwhelming majority of the engineers in fact. This leads to a provincial, arrogant company culture. The amount of time you have been at SpaceX and how long the people in your personal network have been at SpaceX are the overwhelming drivers of your reputation within the company. Many people like to sit around and talk about the good old days and how things used to be so much better. This is likely untrue, counterproductive, and isolating to people who weren't around at those times. There are many people who will vigorously deny that there is anything wrong with the company culture. This attitude stands in the way of changes being made for the better. There is a lot of pressure to take on as much work as you can possibly handle without showing signs of failure. It is preferable to be running 3 projects and getting a C- on them than to run one project and get an A on it. If you aren't obviously failing or complaining to your leadership about the amount of work you have on your plate, you will be handed another project.