If you simply purchased the USB drive and started using it with your Mac right away without reformatting it first, then the drive is most likely formatted in the FAT32 format, which has quite a few limitations that sometimes conflict with file-naming conventions on the Mac.
For example, you can't put a file larger than 2GB on a FAT32-formatted drive. You also are limited in filename lengths as well as valid characters in the filename. In the past, file metadata that the Mac operating system used wasn't transferred properly to a FAT32-formatted drive... which isn't so much of a problem anymore with the newer versions of OS X, but may still cause general "funkiness."
If you plan on only using this drive with Apple computers and the Mac OS X operating system, I would highly recommend backing up your data already present on the USB drive, then using Disk Utility to reformat the drive to the HFS+ format, which is OS X's native file system format.
If using this drive solely with Macs and OS X is not possible and reformatting to HFS+ is not an option, then I would recommend doing an old-fashioned "smell test" on the files you're copying to the drive. Do they have relatively long filenames? Are they huge files -- around 2GB? Do they use any "questionable" characters in their names, such as slashes, quotes, colons, or any "symbols" (like percent sign, dollar sign, etc.)?