I've actually gone through the interview process twice with SpaceX. Once for a direct-hire position at the home Hawthorne CA facility and a contract-to-hire position at the launch complex in Cape Canaveral FL.
The direct-hire interview process involved 3 phone interviews that increased in length and complexity. After satisfying management over the phone I was flown (all expenses paid) to Hawthorne CA for a 3 day period. The on-site interview was roughly 6 hours and involved being interviewed by no less than 8 people. Current toolmakers, planners, designers, management, and even other department heads. They all came with their own angles and loaded questions. Certain people wanted very general answers while others wanted specific job-related technical questions. In the end I wasn't selected for this position.
I ended up at SpaceX anyway when 8 months later a headhunter firm contacted me about contract-to-hire positions out at Cape Canaveral. For this there was a single interview that involved mostly technical questions specific to the job. With that satisfied the position is then treated like a contract. I was given a dollar amount and told to come to Florida. Once there I was told to prove myself over a 90 day probationary period. If things worked out I would be offered a direct position with the company. I worked my butt off and in 3 months I was rewarded with a blue badge as a direct SpaceX employee.