By any chance does this system happen to have the ATI X1900 video card in it? If so, that thing was a real turd, and actually the replacement was, I believe, from nVidia's problem line of the 8800GT.
In any case, the ATI card had a pretty high failure rate, but not enough that Apple has any sort of extended repair program for them.
But it could be a couple of other things to, so fish out your restore media and find the one that has Apple Hardware Test on it. Run that, the extended version, and see if it finds anything else. If not, I'd be willing to bet a shiny nickel you've got a video card that is about to crap out on you. So, you can either call Apple and ask nicely if they would be willing to create a one-off exception to your warranty and get you a new video card. If not, start looking to see what video cards are supported in 10.6 that won't overtax your PSU.
It may also be time to have someone take off the heatsinks (I just replaced the logic board on one of these systems like 2 days ago, and trust me, you don't want to try this yourself, because it requires some difficult to find tools... Like an 3mm hex driver with an 8" shaft) and redo the thermal grease. It's also possible one of the fans for the CPUs aren't working. That should be picked up by AHT.
Model Name: Mac Pro
Model Identifier: MacPro1,1
Processor Name: Dual-Core Intel Xeon
Processor Speed: 2.66 GHz
Number Of Processors: 2
Total Number Of Cores: 4
L2 Cache (per processor): 4 MB
Memory: 6 GB
Ever since upgrading to the latest OS, my Mac Pro chugs along fine for several hours of use (or over an entire weekend just idling) then eventually starts to develop graphical glitches that coincide with serious unresponsiveness. Once this sets in, its usually only a matter of a few minutes before the system locks up entirely and must be restarted.
Here's what the screen looks like when things start to get weird:
http://tinyurl.com/2fvbas6
I run a lot of programs at once -- many Adobe CS3 apps simultaneously, for example, along with iTunes, Word, Safari -- but it's unclear whether any of those is a common factor when the problems occur.
The console reports:
Date/Time: 2010-12-16 12:44:41.722 -0800
OS Version: Mac OS X 10.6.5 (10H574)
Report Version: 6
Exception Type: EXC_BAD_ACCESS (SIGSEGV)
Exception Codes: KERN_INVALID_ADDRESS at 0xffffffffffffffe8
Crashed Thread: 2 Dispatch queue: com.apple.awacsd.GCDispatcher.q
and
Process: awacsd [32]
Path: /usr/sbin/awacsd
Identifier: awacsd
Version: ??? (???)
Code Type: X86-64 (Native)
Parent Process: launchd [1]
Date/Time: 2010-12-16 15:54:16.159 -0800
OS Version: Mac OS X 10.6.5 (10H574)
Report Version: 6
Exception Type: EXC_BAD_ACCESS (SIGBUS)
Exception Codes: KERN_PROTECTION_FAILURE at 0x0000000101e000a9
Crashed Thread: 2 Dispatch queue: com.apple.awacsd.GCDispatcher.q
Crap, it's starting again now...
Any suggestions or thoughts?

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