jkOnTheRun has a great trick for cleaning the Mighty Mouse trackball:
First slightly and carefully moisten the ball, I used spit on my fingertip. Then take a clean sheet of paper and turn the Mighty Mouse upside down. Run the ball rapidly in all directions on the paper. In about 5 seconds my problem was fixed as the dirt worked itself loose and came out on the paper. I love my Mighty Mouse again.
Check out the posting for more details and some suggestions in the comments. – Link