Media Production managers must be highly organized to be able to handle many tasks at once, must have strong communication skills so they can work with different departments and well understand their different needs, and must have problem-solving abilities to be able to resolve daily issues that may arise whether they are technical, logistics, budget related or other.
A media production manager should be a team person since he will be the one guiding the production team, he should be talented when it comes to supporting and communicating with his team. He should also have advanced analytical skills as well as multitasking, and diplomacy skills.
I think that a Media Production Manager should have the ability to handle a variety of industry-related software. I imagine that this field can be quite hectic, so he/she should be well-organized and with good time management and project management skills.