I had the same problems! I don't exactly know what cured the problem for me... but the only thing I can think of that could have done it was setting custom resolutions in init.cfg. I set the resolution of the game to match the screen ratio of my widescreen monitor (16:10). That worked fine, but I noticed something weird, setting widescreen resolutions had an odd effect on my framerate, even at 1280x800. So I tried setting the resolution back to one of the the defaults, which gave me a large boost in fps and for some reason the graphical oddities were no longer there.
So, what I'd suggest, after updating your vidcard drivers of course, would be to set a custom resolution in init.cfg. One that matches your screen ratio. Test it out, if it works fine that's great! If you find you're getting bad fps, switch back to one of the default resolutions and hopefully the graphical problems will be fixed! I really can't think of any way why this would make sense, but nonetheless I hope it helps!!