Episodes like Threshold and that one where the Enterprise crew turn into children come to mind. The latter actually involves transporters.
They don't usually revert the crew using the backup data, though. They just program it to make changes to their bodies, like removing things. It wouldn't be any stranger than removing an alien pathogen.
The backup data, I think was only used for Pulaski when she got the ageing disease (where it might have been a reference pattern to correct errors, and they had to actually compare with a known good genome), and for Tuvix.
We do also know that a bad transport can't just be retried either. The Motion Picture had a transport go wrong, and Starbase One couldn't just restart the transport with backup data, or repair what they got back. Similarly, Scotty couldn't just load up Franklin's backup from the Jenolan's computers and transport him in either.