Either the problem is gone or else I've just bypassed it by what I did, but the past 2 days have been without problem.
I reversed the USB cable connecting the Buffalo external HD to my iMac and swapped ports on the hub. I also re-indexed Spotlight.. but I also removed the external HD from indexing. By the way I have two external hard drives.
TM hasn't reported any problems backing up successfully since then.
But there is this curious Error message in Console near the end of the backup process, each time it's been done in the past two days. If you don't mind looking at it, here is the error message within its context:
8/21/13 6:37:39.199 PM com.apple.backupd: Starting standard backup
8/21/13 6:37:39.318 PM com.apple.backupd: Backing up to: /Volumes/TMBackups/Backups.backupdb
8/21/13 6:37:43.438 PM com.apple.backupd: 327.3 MB required (including padding), 708.51 GB available
8/21/13 6:38:22.526 PM com.apple.backupd: Copied 2042 files (11.7 MB) from volume Macintosh HD.
8/21/13 6:38:22.720 PM com.apple.backupd: 313.2 MB required (including padding), 708.49 GB available
8/21/13 6:38:26.352 PM com.apple.backupd: Copied 625 files (33 bytes) from volume Macintosh HD.
8/21/13 6:38:27.204 PM mds: (Error) Volume: Could not find requested backup type:2 for volume
8/21/13 6:38:27.205 PM com.apple.backupd: Starting post-backup thinning
8/21/13 6:38:27.205 PM com.apple.backupd: No post-back up thinning needed: no expired backups exist
8/21/13 6:38:27.290 PM com.apple.backupd: Backup completed successfully.
Is all's well that ends well ("Backup completed successfully")?