What skills do you need to be successful in the Operations department at SpaceX?

Ability to adapt, debate (w/o being an a**), comprehend others ideas and work with the team. The most difficult situation one has to deal with at SpaceX is the mashup of backgrounds and personalities. In alot of the rocket industry you tend to notice a trend where as the personnel working together have similar backgrounds, where SpaceX employees could have been sheet metal workers but now work in propulsion. Someone who was a tire tech at a Big O tires is now running avionics. Having the ability to work along side someone who doesn't necessarily hold the same background as you is what makes operations the most challenging and requires a skill set of patience and adaptation. That and when you find out your years of swapping parts, systems and running maintenance for squadrons means you'll start at 18-20$/h, you'll need to bring your skill of sitting down and rotating.

Being able to work through the minutiae and work the required mandatory overtime which will provide you with a undesirable work-life balance

Never disagree even when you know you're right