Huzzah! I just fixed my Mighty Mouse, which unfortunately could not scroll down. At first, I tried taking it apart, and got through the first step, realizing I was not skilled enough to continue without breaking it.
So, I searched around the internet some more (with a different mouse), and found various sites and tips. So, I took a wet towel, and wet the mouse, including holding the scrollwheel in place, while I wiped it, and then moving it and wiping a new dirty section. Then, I took a very tiny amount of hand sanitizer, and scrolled with that finger. Then, I wiped it off with a wet towel, and used my other hand to dry it.
I then tested it on my computer for a minute, and found that if I clicked and scrolled it would work decently, and much of the time it would work correctly. However, it still didn’t work like it was new. So, I did the whole hand sanitizer thing again, and now it works perfectly.
Heh, w00t.