I'm actually having a similar "problem" with my fiance's Viewsonic VX2035WM.
Here are her specs:
Intel Core2Duo E6400
2GB RAM
Radeon X1950XTX (using DVI connects)
Gigabyte 965P-S3 motherboard
Windows XP MCE
A few interesting correlations appear similar between our two systems. First, we're both using DVI, and second, we both have this issue with an X1900 series card hooked up to a Viewsonic monitor. I've noticed several points about the mysterious dots that stick out, though.
1) Likelihood of appearance is highest when the monitor is coming from a dormant state.
2) The dots do not appear harmful to the screen itself, but they sure are a nuisance.
3) Mine are green, actually. I've yet to see blue dots, but it may be a function of some as-yet discovered aspect.
I was playing around with her computer one day and, completely on a whim, upon encountering the green dots switched the desktop color depth to 16-bit. After the black, the desktop flashed back up and, to my surprise, the dots were gone. Puzzling, no doubt, but 16-bit colors just feels so archaic, so I clicked "No" when it asked me if I was sure I wanted to keep these settings. Oddly enough, the dots were gone from the remainder of the time I had the monitor on. I did not get to check later if they had resurfaced, but as a temporary fix, my session was dot-free.
Theories:
1) Handshaking? DVI does quite a bit of voodoo with HDCP, as I understand it, and it's possible that it's missing a communication at some point in the early startup process.
2) DVI cable? I'm hesitant to push this one, though, because I'm assuming you're using the packed-in DVI cable that came with the monitor. Two people with bad DVI cables from the same company with near-identical monitors is a coincidence that seems far-fetched.
3) Drivers? Hey, never hurts to keep those babies updated.
If you've made any progress, davidos, I'd love to bounce ideas back and forth. I've advised her to try the 7.3 Catalyst drivers, which were released not too long ago. I will report our findings.