Having worked in film/TV production for several years, I'd say the single most mandatory skill to have is: problem-solving. If you're a good problem solver, people will want to keep working with you. They'll need Naysa around for when things go wrong (things always go wrong! especially in film production!).
Say you're scheduled to film a documentary about a certain star basketball player, but you find out the day of the interview that something came up, and she's got to be somewhere else that day. You've got a huge crew, and tons of film equipment, but no star athlete - what do you do? Maybe you call everyone else who is going to be in the documentary and see who else can get to the studio asap to do their interview instead. Or you send some part out of your crew to film neighborhood kids playing basketball, so you're at least getting some footage for that day.
Other problems I've seen: people come up with a budget for a project, only to find out they have to cut that budget by a third - where do they cut the corners to still make what they want to make, with the money they have? Or someone makes a shooting schedule that is two weeks long, only to find out they have to get the job done in one week. Production is really all about problem solving - and good problem solvers are usually creative thinkers, able to stay calm in a stressful situation, and kind to others even when they're under the gun (that last one is a big one - everyone wants to work with KIND people, especially in stressful situations).
Hope that helps! Kendall