I'd do a DBCC CHECKDB of all the databases. Also try a backup to a network drive or another physical drive if that's feasible to see if you still get the same errors. You might even want to try just another location on the disk you are using for your backups.

The windows event logs would be the other thing you would want to go through since that error is usually thrown from Windows due hardware issues. If you get the error again, I'd check the windows event logs for the time of the backup error as well.

Sue