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!
Here are some skills that I believe are important in the production/film industry:
-Being a good communicator
-Good writing skills
-Being a creative/visual storyteller
-It helps, or sometimes makes the jobs more fun, if you enjoy or are knowledgeable about what you are working on. For example, If you are want to work in the tv sports production field, it may be a good idea to watch games on TV and start to see the different things you notice about an on air broadcast. You could also do this when it comes to films.
-In the production field, I've also come to learn that experience is very valuable.Take as many internships or shadow opportunities that may be available and never be afraid to ask someone to mentor you if they work in the field you want to.