Well, well, well... I've found some new friends. Guess who also has an ATI HD4870 and is having the same problem. Nice to know we're not alone in this world.
It isn't just texture and FPS problems though. My view is "twitchy", sometimes flipping rapidly at 90 degrees in a strobe-like frequency... Which might be a good thing because I can see who's about to shoot me in the back!
The game is pretty much unplayable for me at the moment.