Pros
SpaceX is an incredibly exciting place to work - it's hard to find a job where fast-paced engineering work leads to incredible launches every few weeks. Interns are assigned responsibilities and projects befitting full-time employees. Although it is a lot of work (you're never waiting on tasks), the skills you acquire from a SpaceX internship are comparable to those that would take a year or longer at another aerospace company. In addition, interns are now given overtime pay and actually limited to 50 hour-weeks. Interns are fueled by free frozen yogurt, free coffee, and delicious (subsidized) meals from the in-house restaurants. If you're passionate about space exploration, the work at SpaceX is progressing at a faster pace than anywhere else. At other companies, you might be lucky to have an internship during a tiny fraction of a mission or development cycle; at SpaceX, you are likely to see multiple missions from beginning to end.
Cons
It's a competitive environment with a lot of the pressure - there is always a lot of work to do. Many employees are young, with few near retirement age, so it can be difficult to be promoted (which is why the high turnover rate also has benefits). Intern compensation is average or above average, but much of the extra income goes into the high cost of living in Los Angeles. Interns who live in the "intern housing" arranged by SpaceX are able to commute to work by shuttle, but rent is very high.