Did you wash the CD? I borrowed a music CD from a friend and he handed it to me with his fingers on both sides of the disk. He said it sometimes didn’t play very well. Gentle wash with warm lightly soapy water, rinse, and dry gently with a fluffy towel. No more skips.
This doesn’t work if the disk is scratched or oddly much worse if it’s damaged on the label side. The music is right under the label.
It also doesn’t work if the disk has a paper label or was printed on an ink-jet printer.