First, my troubleshooting technique was to use Retrospect to browse the volume that was causing this problem to confirm that I could reproduce the error. I then created a subvolume for every folder in that volume and used browse on each to find which of those was causing the problem. Repeat until you find the culprit.
I did not track this down to an individual file. I did, however, track it as far as this path:
/Users/<username>/Library/Caches/Metadata/Microsoft/Entourage/2008/<username>/Attachments
This user has a VERY large Entourage database, and recently we rebuilt the search options for Entourage. Clicking the "Include attachments…" caused Entourage to make a copy of every attachment in the path above. That "Attachments" folder had 45,000+ folders in it. And, unfortunately for everyone, I wasn't planning to create and test 45,000+ subvolumes. I've turned off "Include attachments…", and now that folder is gone. And now, Retrospect can scan this volume for backups again.