Pros
There is never a shortage of interesting hardware projects. Involvement in and impact on projects is more a function of your ambition and less a function of your time at SpaceX or any other experience, making it a great place for recent graduates to grow as engineers. The president is great; in particular she excels at managing difficult people and situations. The CEO has strong vision and harshly scrutinizes important company decisions.
Cons
The expectation of low-level design engineers has ballooned with time and is currently at an absurd level. Low-level engineers are almost always held responsible for mistakes that middle managers should have prevented. Your performance is judged without consideration of outside factors; team building is largely nonexistent. If SpaceX was a football team, they'd assign the quarterback as a receiver and fire them when they consistently dropped the ball. There are tracks for management and technical expertise, but there is not any support for growth in technical areas. Learning is assumed to be a self-motivated activity that occurs in your own time. The CEO is difficult to work with and seems unable or unwilling to change.