OK, you know how to get new missions to show up, you need to clear other ones? Well, I beat the game a few days ago, and now I've reached a point where there's no battle missions, and all the dispatch missions require items that I don't have. Is there another way to change the missions?

Yes and no. If the dispatch mission has an item you don't have, chances are you threw it out earlier without realizing. Beating those missions is one way to make more appear. Second way is to accept a mission(prefferably one you cleared) then cancel it. This will force other missions to appear on the list. However, since the majority of the battle missions are done with ease, they don't get repeated often. Only a select few get repeated.

But they all require an item that I don't have, and there are no battle missions, thus I can't just take one and leave on it. *sighs* Maybe I'll just restart. There goes my chances of ever getting Cid in my party.