It just sounds like a bad burn/damaged disc. There's a new program called ISOPuzzle that does a good job of copying damaged discs, you could try that. It will copy the disc to your HD as an .ISO image file, an exact copy of the full disc. You can then burn that.
What kind of disc is this BTW? Is it a store-bought disc, or is it something that's been burned? Is it a game? If it's a game, it might be some kind of copyright protection but I'm not familiar with specifics of game copyright protections.