[webber]

what you need to do is get yourself some Son of a Gun protector made by STP it is a high density polymer which will bond with (with its plastic properties) cd surface use a soft chamois to wipe it in and rub.
i use this on my palm IIIxe screen to fix scratches, i don't know if it will repair what you have done with toothpaste but that is a definite no no to do.

regards
webber
i live in canada so if you can't get this i will list some other products such as armor all protector etc...