I've gotten a classical music piece into my Touch, but it's in "songs" not classical, even tho I moved it into "classical" on the computer.
How do I fix this on the Touch?
You could try editing the Playlist in your iTunes and then using Sync to transfer those changes to the iPod. If that fails, remove the Playlist from the iPod (by deleting it in iTunes and then Syncing) and start again.
If you want to start totally from scratch, you could do a Restore, which will remove evereything from the Touch and then put back only what you have set in the iTunes Library. Restore is a bit drastic though. It's done by connectin g the iPod to iTunes and on the Device/Summary pane, selecting Restore.
It can take a while to complete and if you have any data (information of your own) on the iPod, such as Notes etc. these will be deleted.