Thank you everyone for posting this thread, as it helped me fix the issue on my bro's computer.
Per Yopachi, first needed to turn OFF "Use Advanced Lighting" - that was creating the glitch all over the place. Then there was still the glitches around objects as most people have been reporting.
Turning off the sky does work, BUT I believe I have found an alternate solution where you can key the sky ON! In Advanced display settings, change the Sky Reflection Update Interval from "Always Update" to "Every 10 seconds". It appears the sky update is what triggers the glitch (you can see the glitch get less prominent as you reduce the sky refresh) and changing to "Every 10 seconds" basically makes the problem go away! Or at least it does for me
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And yes, like everyone else on this thread, the computer has an ATI video card.