Cleaning the Apple Mighty Mouse
This post is just to help people with a similar problem - hence the search term friendly title.
There's a problem with the design of the Apple Mighty Mouse, in that it tends to gather in dirt under the track ball. This means it doesn't scroll, sometimes in one direction, sometimes in more. It's impossible to get under the track ball without dismantling the mouse, and then dismantling the track ball carriage - and then it's almost impossible to put it all together again. Needless to say, this will void your warranty.
There are a few HOWTOs out there explaining how to perform the above process, but as my mouse was under still under warranty I gave Apple support a call. They advised me to dab the track ball with a wet finger, turn the mouse upside down, and then roll the mouse / track ball around on a clean, white piece of paper. It worked! My mouse trackball now scrolls in all directions.
So I recommend you try that before getting out your screwdriver...