OK, this is an esoteric one, but I’m happy to report there is a simple solution.

We migrated Stacy over to using Thunderbird (from Outlook Express) on her Mac to cut down on the spam. In the process, we upgraded her to OS X.
Strangely, while POP connections to our local QMail server are nearly instantaneous on the Windows machines, there would be a 30-40 second delay for her. It wasn’t a Thunderbird problem — we could replicate the problem by telnetting to port 110 — and only from the Mac OS X machines.

Karl finally succeeded in diagnosing the problem. QMail uses tcpserver to wrap connections. tcpserver, in turn, checks back via ident. The Mac OS machines don’t have identd running by default. By running tcpserver with the “-R” option (disabling the ident lookup), everything works brilliantly as it should.