You might already have known that a CD will malfunction and won't be read properly by the player if it has some dust or dirt sticking on the surface. This is why it is advised that you wipe the CD surface (the side opposite the one with the label, where the data is written) with a clean cloth to wipe away impurities that obstruct the laser of the player from reading the data. If after doing this it still doesn't work, you could get some alcohol, spray some on a tissue and gently wipe this on the CD surface.
This technique might not work each and every time, although personally I tried this and it did work. I was copying some files from an old CD and there was this particular file that cannot be copied because it cannot be read from the disk. After several failed attempts, I tried the said technique above, and voila it worked! I was able to successfully copy the file. :D
Sometimes, just being clean would to the trick. Hope this post helps! ;)