you might or might not be relieved to hear that i had the EXACTLY the same problem as you have right now. This was on a Mitac 8355. TBH I should mention that I did do a mild o/c on the video card. But then again ATi Tool was reporting 0 artefacts and so I kept going
Anyways, here is a hint to the root of the problem. Turn off the machine and let it cool down. I dunno, give it 1 or 2 hrs so that it is completely cooled down. Now turn the machine on and see if the green pixel-like things are still on the desktop. My guess is it won't be. Now run a graphically intensive game. For about 30 mins or so. You would probably find that the green suckers slowly start to creep back again.
I believe that this problem was caused by too much heat. Because when this was happening to my machine, I paid careful attention to the fan speed of the laptop.
When the fan went from LOW > HIGH, most of the green patches would disappear.
But going from HIGH > LOW again, causes them to re-appear. I got the fan to kick in and out by running ATi Tool and closing it again. It basically puts load onto the cpu so that the fans need to kick in.
As far as i'm aware, this is a hardware issue and so the laptop needs to go back. Sorry
probably not what you wanted to hear.