So back to the business of the day: scheduling yourself. Seeing that your days could be filled with meeting after meeting, you need to be hyper aware of your short- and long-term goals and how to fit in what you need to get done in order to accomplish these goals. This means you should have a daily calendar in which you list all of your meetings and, in addition, have some sort of system of tracking your to-do list and checking each task off as you complete them.
As an assistant, it's typical to have a letter- or legal-sized note pad on which you list all of your tasks that need to get done. As you finish a task, a good idea is to highlight it so you know it is complete but you can still read it. That way, you can know at a glance that you did address that task and it is done. There's nothing like trying to read a now unreadable, crossed out task as your boss is standing over your desk and wanting know the status of the job -- so best to keep them readable as you check them off. Your to-do list can be a long running list that can be added to on a daily basis or you can rewrite your list each day or week (removing those items you already finished -- though keeping them accessible if you need to give a status report). Personally, I like to rewrite my list periodically as it helps to remind me to get those long-gestating tasks done.
Being a film producer comes with a million tasks and it's impossible to keep everything organized in your head. Our memories only go so far. And it may take time and a lot of trial and error to figure out a system that works for you. So don't get discouraged if you find yourself getting overwhelmed by the large amounts of work to be done. Take it day by day, task by task. Prioritize everything, while making sure to fit in tasks that address your long term goals along the way. In no time (or it will feel like no time because time moves fast in Hollywood), you will look back and be amazed at how much you have accomplished.