MacBook Pro repeatedly freezes, often with odd display glitches I have an older, 2007 15-inch MacBook Pro (model identifier MacBookPro3,1)  which has begun freezing repeatedly. 

If I boot into Single User Mode it stays operative, however I've begun to get graphic glitches here too:

 

Booting to the Mountain Lion recovery partition, a disc, or any other graphic interface I get a freezing hang. This is often before the machine has booted completely.

At other times it will repeatedly reboot.

I have reset SMC and PRAM, and run fsck -fy on the drive. 

I should also note that the machine generally kicks up its fan pretty quickly and runs very hot, even in Single User Mode, so I am suspecting overheating, perhaps brought on by the video demands?

Does anyone else have a guess at this and/or another diagnostic step?
The symptoms you describe could all be explained by a failing GPU system but before seeking a hardware repair (or quote), I would try reinstalling a clean version of OS X - perhaps the original version that shipped with that Mac to ensure that the hotness and slowness isn't because of added load the new OS has provided and actually something relating to hardware cooling or heat generation.

Your picture is very telling as well.

The three things that hardware could fail are:


LCD panel and cabling
GPU itself
VRAM


The patterns you show in single user mode could either be software or hardware. If it's hardware, they will get worse over time (perhaps dramatically worse) and we've already covered the software angle. Usually when the hardware is faulty, you can get poor graphics in single user mode or the boot selection screen - so you might be right it's overheating / the hardware starting to fail.