I’m willing to bet your X1900 XT is dying a heat-related death. My first X1900 XT died within 9 months and Apple replaced it under warranty. When the first card died, I was seeing pixel artifacts exactly like what you describe. The replacement X1900 XT has been working fine since I got it, but it has still been hot and loud.
I just bought the ATI Radeon HD 4870 upgrade for my 2006 Mac Pro last week. Apple doesn’t list the card as officially being compatible with the 2006 Mac Pro, but it works just fine as long as you’re running OS X v10.5.7. The 4870 uses both PCIe auxiliary power connectors on the motherboard, so if you’re currently using two graphics cards that both need aux power, you’ll lose that ability if you upgrade.
I’ve had zero issues since upgrading, and the card is working great both in OS X and Windows XP under Boot Camp. For all intents and purposes it’s the same as the X1900 XT in OS X, only with the advantages of being much quieter and not needing regular cleaning of the heat sink vanes.
The 4870 absolutely slaughters the X1900 XT in Windows 3D gaming performance.
By the way, I’m using two DVI monitors with the card – I purchased the Mini Display Port to DVI adapter and it works perfectly.