Apple has released an updated technical support document on the proper way to clean your Mighty Mouse. As much as I like my Mighty Mouse, I do have to clean it way more often than I ever had to clean my other mice like the basic two-button/scrollwheel Logictech one that I've been using for years. The most annoying problem with the Mighty Mouse is that it seems to very rapidly pick up dirt, grease, and other undesirable crud from my mousing surface. I clean my desk at least once a week with alcohol wipes and elbow grease, so it's not overly dirty.
I agree with Apple's document that the lint-free cloth is a good way to get fingerprints off your mouse. Sometimes I'll just use paper towels and some iKlear display cleaner which seems to do a pretty good job of cutting through the crud. I've also, on many occasions, had to "vigorously rub" the scrollwheel nub while holding the mouse upside down to dislodge something that's causing the scrolling to not work properly.
Apple's even posted a video tutorial on how to clean your Mighty Mouse.