I have snooped around the net and found the earliest days of Mountain Lion's release had a panic about incompatibility with those early MacPros. Later posts show that there are people with MacPro 1,1 that CAN run Mountain Lion's preview and those that can't.
Those that can't might be using the original or inadequate video cards, according to other critics on the net. Good news, though: if people with MacPro 1,1s are running Mountain Lion successfully, it means all MacPros can run it and there is something causing inadequacy or incompatibility.
However, we have to be aware that our machines are definitely closing in on antiquation, in terms of OSX support. Once we get to the last OSX, we have maybe 2 or 3 years and nothing more will be made by Apple to help us adjust to blossoming technology and formats.
If Mt. Lion supports us, the next one probably won't. So our Mac Pros will probably be best replaced by 2015. That's 9 years! A brilliant life span, I think, for such tech. Who today can still use a 2003 PowerMac without trouble? My old 2003 PowerMac was already a clunker when I sold it years back.