I've played with ddrescue very lightly. From the GNU webpage linked above, it appears it creates logfiles which can be examined:
Ddrescuelog is a tool that manipulates ddrescue logfiles, shows logfile contents, converts logfiles to/from other formats, compares logfiles, tests rescue status, and can delete a logfile if the rescue is done. Ddrescuelog operations can be restricted to one or several parts of the logfile if the domain setting options are used.
That might allow for identification of files with bad sectors.
That would need either a hook to the kernel or a file system parser.
Even if you manage to do that, I'm not sure it would be a good idea to continue to use a file system that has lost sectors, even after fsck. Are you sure fsck is fixing any inconsistency? Are there any automatic procedures in place that guarantee that the fsck algorithms are in sync with the actual file system code? (Answer anew for any file system I might be using.) You definitely should do backups by reading the actual files, not the underlying device; perhaps in this case it could be OK (since it was a backup itself already, hence a copy of life data; but then if OP bothered enough to recover the files, maybe he'll bother enough to make sure they stay recovered?)
Ddrescuelog is a tool that manipulates ddrescue logfiles, shows logfile contents, converts logfiles to/from other formats, compares logfiles, tests rescue status, and can delete a logfile if the rescue is done. Ddrescuelog operations can be restricted to one or several parts of the logfile if the domain setting options are used.
That might allow for identification of files with bad sectors.