Pros
I'll be frank: if you are after a challenging engineering problem, there are very few companies offering the challenges that SpaceX can offer. The feedback loop on your designs involves flying a sapcecraft/rocket, and there is no sweeter feel than seeing your contribution perform in the complicated mechanical orchestra that is flying spacecraft and launching rockets. The amount of responsibility a young engineer is given can be claustrophobic at times, and its most definitely sink or swim. But as you start finding that stroke and swimming, you'll find what SpaceX wants you to: the self confidence to solve problems that you search out and find. You need to learn modal FEA? Here's the license, figure it out. Production struggling with making your designs? Straighten it out. The berth that you are given is wide, and the expectations are high. One engineer (that has since quit) once told me the best part of his day was driving by another aerospace company and knowing that he personally is accomplishing the same amount as 3-4 engineers anywhere else. We are doing awesome things every day, and being offered a job at SpaceX is a big deal, the only question you'll have to answer is "How much do i want to sacrifice to have these cool problems?" The heyday of the small sexy spacex is long gone, but the challenges and opportunities to solve them haven't disappeared.
Cons
Zero career development. Very long review process. Lower pay compared to industry contemporaries. Being held accountable for problems out of your control. Work life balance can be good in a lull, which rarely happens. Very large chasm between management and boots on the ground.