After some experimentation I have proven my hypothesis that the problems are related to the damaged databases -- depending upon the problem, people's entries in the databases have no corresponding entry in either the password file, the bio database, or the plugins databases.

This is easy to fix on a case by case basis, but there are so many complaints that I am writing a script to fix the approximately 15,000 profiles affected by these problems. This is my main focus for this weekend -- email is secondary but will be worked on as well.