The return code of a backup (say if you ran a "dsmc i" from the cmdline) will tell you if it was successful of failed for some reason. But you have to understand what it considers a success and what it considers a failure. If you're backing up 200 files and 2 were not backed up because it skipped the files because they were open by a process, it will still consider that a successful backup. The only real way to be sure that a given file was backed up is to do a dsmc query backup for that file or group of files and see if ineed the TSM server has that file backed up.
So it depends on what you're trying to do. If you do a "dsmc backup gerald.txt" and it returns successful, you can be assured that file was backed up successfully. If you're backing up an entire filesystem though, you have to be a bit more careful about the results by checking the dsmsched.log file and verifying it backed up what it did or the results of the backup to see how many objects failed or otherwise did not get backed up.
hope this helps..