Skips with CDR's

I purchased a used Cary 303/200 in great condition. This thing sounds great, but I seem to have problems with skipping when playing CDR's. My CDR's are not kept in jewel cases and are not super clean. They also have some scratches and some skip more than others. I didn't have this issue with other players. Is this normal? I opened it up and wiped the laser with a cotton swab, it made no difference.
I love this thing but this drives me crazy. I almsot posted it for sale, but I thought I would throw this out there very any other advice on what else I can do besides play only store bought cd's.
Thanks in advance for your help
Jeff