Choosing your mouseObviously, the mouse you use is the most important tool you can have in this wonderful game (besides your mind), and you should take great care in choosing one. I don't care what anyone says, there is no way to get a competitive score using those "alternative pointing devices", such as a trackball, trackpoint, touch pad, etc.. Another point to remember is that if you have a 3-button mouse, you can use that center button to clear around a square instead of using the left/right buttons. This has the potential to increase your speed as well as your accuracy. (it will also give you the chance to exercise one of your other fingers)
Mouse MaintenanceIn my sweeping experience, I have found that it is most effective to configure your mouse to a fairly slow tracking speed, and non-accelerating. Use of a good mouse pad is also highly recommended. Above all, you MUST keep your mouse clean! Every so often, you should take the ball out, and clean the rollers inside the mouse. Get rid of all that pocket-lint-looking stuff (use a toothpick or similar dull tool. I like to use the tweezers from my swiss-army knife).
Good luck with your sweeping!