Sounds like this has been a problem for a lot of people around teh Internets (although VPrime proves that it isn't universal).
I contacted Destineer support, and they came back with the following advice:
"Try uninstalling the game, then delete the 'Unreal Tournament 2004' folder from /Users/<your user name>/Library/Application Support/ and then reinstall the game. After reinstalling the game, apply the 3362.9 update and the game should work properly."
For us Mac users, "uninstalling" is high-fallutin' talk for "drag to the trash," of course. I can't find any programmatic uninstaller.
I did this, and it worked for me. (You'll lose any single player game progress, etc.) Hope it works for others as well.