I found that it had a very slow dribble-leak from the steel nipple fitting at the top of the tank on the 'out' (hot) side. The reason for the ceiling damage was that the morons that installed the drain pan barely tightened the PVC to the pan and didn't use any sealer whatsoever.
I sealed up the pan and then got to work on the leak. I unsoldered the copper so I could work with the steel fitting. I removed the fitting and the threaded copper adapter, which were pretty corroded, so I replaced them. I used plenty of teflon tape on the steel pipe threads and cranked it down to spec: "dang tight". I then soldered the copper back together and let 'er rip. No problems for several days, but...
Last night I checked the ceiling and it was dry. I then went up to check the water heater and sure enough, it had an identical leak! (ARGH!) It's dribbling from the base of the steel nipple fitting right where it threads into the top of the heater.
Any ideas how to stop this freakin leak? I've got the fitting tight enough that I fear if I try to put another turn on it I might strip or split it, that is, if I'm able to get it that tight at all. It's really tight now.