Okay, I've been getting good gameplay, only a few crashes until I tried to do the Mutant Bash tv thing.
I do the first part fine, the second part fine, but then at the "Bonus round" part It either crashes while I'm shooting the target, or just after if I screw up.
I've done it about 5 times now. I tried changing my resolution lower, still doesn't help.

Has anyone else had this problem?
Is there any way to fix it?

Yup. I had this exact problem. No crashes, using the 11.9 drivers with Catalyst A.I. turned off until that point. Musta tried at least 20 times, and if I would pass that part, it would still crash when I exited the level.

I suppose I got lucky. I installed the new drivers 11.10 beta whatever with AI off and dropped rez to 640 and managed to get through it. Then reinstalled the 11.9 drivers. It's all a pain in the @ss. I've never seen an Id game so f*cked up.