Disable any proprietary mouse drivers, and make sure you have the latest version of game sprockets from Apple...it will update all of your USB input device drivers. It's on the Apple support page for download. If that doesn't work ,then you might try USB Overdrive, you can find it at versiontracker.com, its a great mouse driver even if you don't need it for a "fix".
I think this should do it, I've used many differnt USB mice on my G4 and all of them worked fine in UT. Logitech, Kensington, M$, Boomslang, and of course that stupid puck all worked fine with UT on my system with USB overdrive and gamesprockets version 1.7.5.
Good luck!