Wet spot under the furnace turned out to be a bad glue joint

Same general area of the house for me, but mine turned out to be the condensate pump rather than a glued joint. Our Carrier is in the basement and the pump sits in a little pan next to it. I kept finding a wet spot on the concrete and assumed the pipe joints were the problem, so I re-cemented a couple of fittings myself and it still came back. Took me almost two weeks of chasing it before I noticed the check valve on the pump was gummed up with slimy gunk, and water was seeping back out of the tubing after each cycle. Pulled the valve off, soaked it in vinegar overnight, and it's been quiet since. The trick you mentioned about drying everything and watching for where the water shows back up is exactly how I finally found it. I used a flashlight and a sheet of paper towel under each suspect spot and checked after a heating cycle. One thing I'd add is that the pump should click on and off on its own during a run. If it seems silent the whole time the furnace is going, that's worth a look before you start cutting pipe.

Mine turned out to be neither a joint nor the pump. When our Lennox got swapped out two winters ago, the installer hooked the condensate line into the existing floor drain, and the drain itself was half clogged with gunk from years of the old system. Water backed up during long cycles and pooled out from under the unit, which made me think the new install was leaking somewhere. I spent a weekend with a flashlight finding nothing wrong with any of the tubing, then poured a bucket of water down the floor drain and watched it barely drain at all. A $10 drain snake from the hardware store fixed it in twenty minutes and the dampness never came back.

Also worth saying, if your furnace has a whole house humidifier mounted on the ductwork nearby, check that too. Mine drips a little when the water panel gets old, and at first glance it looks exactly like a furnace problem.

As for the warranty angle, good on the original poster getting it covered. My installer charged me a trip fee even for the re-cementing fix on a fitting I found myself, so I've learned to at least eyeball every connection before picking up the phone. Saved me one visit already when a clamp on the drain hose just needed a quarter turn tighter.

Whenever I hear a joint had glue on it but never bonded, my first suspect is old cement. I helped my brother redo his condensate run two years ago and the can of cement in his garage had gone thick as honey, barely brushable. Grabbed a fresh can, wiped both surfaces clean, gave it a twist going in, and that run has been dry ever since. My own furnace makes enough water on a cold day that even a pinhole weep will dampen carpet within a cycle or two, so I never ignore a mystery damp spot. Curious if your tech mentioned how old his cement was, or if the fitting just never got pushed all the way home.

Glad yours was an easy fix. Mine wept for months before I figured out the real problem, the installer had left the line running tight against a joist and the fitting was under stress the whole time. Recementing it just bought me a few weeks each time. Had him come back and reroute with a bit of slack in the run and it's been dry for two years now. So if anyone's joint keeps failing after a redo, check wether the pipe's being pulled or twisted into place.