yes, the old sticky labels can often cause such problems - I've been through my collection and listened to these older discs and ripped those
that still play to wav files.
There is software - exact audio copy is one version - that can sometimes pull the audio from such discs...though the success rate can vary.
otherwise you might email other people you know who might have the same disc and see if they might help....
Sometimes a wav rip from iTunes and reburn onto a clean CDr will work, if the problem is just an occasional skip. I also have an old CD recorder that can sometimes dub a copy onto a clean CDr, though if the dye on the original CDr is damaged, you're probably out of luck.