After searching around the internet for a while, I found a bunch of people complaining about their squeaky Mighty Mouses. Some people recommended applying pressure/prying the base of the mouse to pop it into position. Apparently, a lot of MMs are not really aligned right out of the box, and the plastic rubs together when you click them. Anyway, I think I managed to fix the squeak. It's been about an hour since I tried to pop the bottom back into place, and so far my mouse hasn't squeaked at all.