I've been having the same problems. This is the first time i've finally found someone with similar issues. I took a short video of one of my problems.
It can get worse than that and better. Usually worse with time. I downloaded a program called ATITool that stops a lot of it ... For awhile. But with time it gets worse no matter what. All drivers are up to date.
I'm starting to think it may not be my graphics card as I have a different one than you. ATI X1900XTX.
Operating System: Windows XP Professional (5.1, Build 2600) Service Pack 2
Processor: Intel(R) Core(TM)2 CPU 6400 @ 2.13GHz (2 CPUs)
Memory: 2046MB RAM
Card name: Radeon X1900 Series
What kind of monitor are you using, if I may ask?