This isn't particularly damaging to the functionality of the card atm but i'm very concerned about it being a hardware faliure that worsens in the future. Over the past three months I have noticed small (maybe 3x3 mm) squares flashing infrequently and quickly (maybe every 3 hours). They appear on the screen in small groups mostly near the edges of the screen and show for maybe a few milliseconds. i have ruled out overheating as this happens when the card is only at about 60-70 degrees C, but you must consider that i am using a dva to vga adapter on the graphics card output. could it be this? or is it hardware faliure???
More about :radeon 6870 small flashing black white squares
Have you tried another cord? Also, make sure they are plugged in tightly. I had a similar issure with tiny red dots and disstortion but it turned out that my cable got loose.
Today I bought a DVI cable for the graphics card and so far everything seems to be fine, but i don't think i've run it enough to see the results. I have noticed better mouse cursor tracking though, so it's still worth it.