I take it you've gone to system preferences/energy saver and set your machine up to dim the screen when there is no activity.
You should try to attack the cause... as you said... you have a very sensitive mouse. Have you gone into system preferences/mouse and set it to be not so sensitive? What is causing the mouse to move when no one is using it. The mouse shouldn't move on it's own. If it does I would consult an ouija board.