Here are some screenshots that clearly capture the problem. First, the Firefly Forest scene on the GeForce 7800 GTX 512 looks like so. Note especially the glow of the green light on the forest floor. Now, look at the same frame as rendered by the Radeon X1900 XTX. The colors on the forest floor take on a rough, salt-and-pepper kind of texture that looks, as I said, like dithering. For those of you who are squinting and straining to see the problem, I've blown up the most relevant portion of the frame to four times normal size. Here's the 7800 GTX 512 and the Radeon X1900 XTX. If you can't see it there, check with your optometrist.
I pinged ATI to see what they had to say about this problem, and they confirmed that were able to duplicate it themselves. They said that the image problems are caused by a bug in the compilation of the shadow shader on the Radeon X1900. They explained that this shader is different than the one used on either the the X1800 or the GeForce cards because it "employs both Fetch4 and 24-bit DST" in order to best take advantage of the X1900's capabilities.
Sure enough, the artifacts don't appear on the Radeon X1800 XT, so ATI's explanation seems plausible.
Pixel shader programs are compiled in the graphics driver, of course, so ATI should be able to fix the problem with a driver update, and that's exactly what they expect to do. We don't yet have any ETA on the fix, but ATI claims it should not adversely affect performance. We'll have to see about that.