I personally have never really had this issue, except with second-hand games. You really do have to be careful in this era of DVD/Blu-Ray gaming though, the information is so sensitive (in fact, I'd almost cynically suggest that part of why we're using plastic disk technology in this day and age [as opposed to full transfer to the hard drive] is because it is so easy to break, thus creating possible extra profits from clumsy people to developers).
Disk repairs are not an exact science, since data is imprinted in a concrete manner. There is always an amount of damage that can't be undone. Ultimately the only quasi-sure method of fixing an issue with scratched data is to get a new copy.
Aby_Z said:
To remedy your issue, go ahead and rent the game... then switch disks. It could probably work.
So YOU'RE the reason why I can rely on rented disks to stop working halfway through. Thanks for your contribution to society.