That is very strange that the 60gb PS3 would have problems. The 60gb uses hardware emulation meaning that there are actually PS and PS2 parts inside of the machine. The 80gb is what I thought would have the problems since it uses software emulation, which means it just has PS and PS2 emulators, much like you get for your computer.
They do occasionally come out with updates that fix some of the emulation problems. I believe the last one was 2.10, so try getting that if you don't have it.
Sony also has a website where you can check game compatibility found below. Hope this helps
http://www.us.playstation.com/Support/CompatibleStatus