Knew that there was a SpaceX branch in Redmond, WA but initially decided to pass on it since software positions listed were related to "inventory management app" rather than things that fly high. As I was interviewing with another company I accidentally learned that they are actually doing the Internet satellite constellation project over here. After that I tracked down the recruiter via LinkedIn and applied directly. SpaceX recruiters are really overwhelmed by work so it required numerous reminder emails on my part to get the process moving.
Based on the other reviews here a few less persistent candidates gave up on the process rather than kept pushing. If you really want this job, I recommend to keep pushing and sending reminder emails until you either get a firm "NO" or the process moves ahead.
For me the process was in 4 stages:
1) Phone screen with the recruiter: basic C++ and data structures knowledge.
2) Technical screen with one of the developers: C++ and data structures, some threading and OS internals
3) 6 hour technical test: C++, data structures and algorithms. Although the test is pure C++ and not specific to Linux, the code will be tested on Linux box. I would recommend setting up a Linux box with GCC and practicing beforehand if you are a Windows guy like me. Use valgrind
4) On-site interview: this one is not standardized and structured like Google/Facebook interviews. Started with a technical test post-mortem presentation to the whole team. Then there were 4 interviews with several questions from different fields. The pattern there is that interviewers pick apart your resume and burrow into your skills and experience as deep as possible. There are a lot of smart experienced people here so they can go quite deep.
You no longer need to write an essay about why you would like to work at SpaceX, but you do need to prepare an "executive summary" of your greatest achievements to be presented to Elon and Gwynne Shotwell for final approval.
Bottom line: know your C++, data-structures and algorithms. Space domain knowledge is not required. Be persistent (you'll need to be once you start working anyway). Do your research on Glassdoor.com and internet - there is a lot of useful information there.
I also recommend reading the recent book by Ashley Vance about Elon and his companies, so that you will have a better understanding of the culture and environment.