I think the greatest skill is a willingness to listen and learn. Facebook focuses on a few things when assessing interns, and one is learning speed. There's not much time to catch up before you start working on your summer project, so you have to be ready to learn quickly. Full time employees have 6 weeks of training, but in a 12 week long internship, interns can't do that. Questions are super important. Don't waste 5 hours on something that would take someone 5 minutes to help you with, especially at the beginning.
Another skill is working with others. People work in teams at FB, and being able to reach out and work with people is an important part of the job.
Of course, if you want to be a software engineer, you have to be able to code, but remember, the internship is a learning experience. I could code going in, but I didn't know the language I worked in all summer and I had barely done any work with apps (I worked on the Facebook iPhone app). I spent the whole summer learning, which is exactly the point of an internship anyways.
I would say the most important quality for succeeding at Facebook is being able to self-start. You will not receive much guidance from your mentor, as you will be expected to make your own progress on your own project. This can be frustrating (and was for me) since it can be very difficult to figure out WHAT to do, when we focus so much on learning HOW.