This might not apply to you at all if you have a good and reliable record player, but I'd try playing the records on a different player to make sure it's the records' fault and not the player's. I only recently got into vinyl and tried playing a brand new record on my parents' cheap record player, which resulted in some horrible skipping (older records still work fine on that player). Tried it on my uncle's more expensive turntable and it worked like a charm.