Hmmm...
I often clean the scroll ball on a mighty mouse. Apple has cleaning info in the
Apple Mouse user guide:
I take a damp paper towel (not wet), and use that for a surface to roll the mouse upside down. It cleans the ball pretty good. Just takes a few tries to make sure you have it as clean as you can.
Is it perfect? No, the cleaning doesn't always help, but most times, a little patience takes you from a mouse that won't scroll, to one that you can use.