Pros
The advancement of rocket technology has been at a snail's pace for some time. SpaceX is trying to push the boundaries to make access to space cheaper, while still being reliable. You get to work in a very fast paced environment where your work actually matters. There is a lot of freedom to give your opinion on how things should be done, which is great, it's not always one person making the decisions. It's inspiring when you read articles that show other companies' reactions to SpaceX and how they are starting to think more about efficiency and not about how much money they can make.
Cons
Some areas of the company can be more demanding and you may end up working longer hours than others, but that's entirely up to how you manage your time.