Ugh, use a lint free cloth and Pledge furniture polish, wipe from the inside of the disc to the outside in straight lines, rotating the disc with your other hand once a wipe is completed.
You are not going to be able to magically write damaged data or create more polycarbonate out of thin air by putting any amount of toothpaste on an optical disc. If a disc is so damaged that the gouge goes into the metal or dyed portions of a disc, then you done fucked up.
Other than that, you can get the disc skimmed, whereby a super (super) thin layer of plastic is removed from the disc, which can help with certain types of damage. However, the shitty home versions of this technique very rarely work.
