I'm not a producer but I recently interviewed one on my podcast which you can find over yonder , and followup
Self promotion aside, from my talks with him, we've come to the general agreement that it's important to display anything that represents your ability to manage tasks and roles under pressure or deadline. Gather testimonials from people you've worked with/managed, have a set of projects that required someone to take charge and direct it in order for the project to come to fruition.
I guess this is kind of vague, but I hope it helps and good luck to you!