I have an mp3 player with a few bad sectors. My problem is that when I try to copy over music files, it'll fill up to the point where the bad sector is, then it'll say "error: failed cyclic ...

Now that you tell me this, i guess "Cyclic Redundancy" is how a programmer would describe an old scratched record skipping on a turntable.

The error you are experiencing is known as the CRC or ‘Cyclic Redundancy Check’ fail error. This error occurs when the data being copied appears to have lost its integrity or is corrupt.