I have a 2005 Endeavor and the car mat on the driver's side only is sopping wet but no rain or water leaking. What could be happening?

Usually what causes a wet carpet is either a plugged sunroof drain or a plugged A/C drain tube. Or worst case scenario is that your heater core is leaking. Never worked on a Mitsubishi, but another possibility could be a bad windshield seal.

Agree,more than likely,Windshield seal,

As a owner of a 2004 Endeavor I can answer from experience. You have a clogged A/C drain. It happens because of a design flaw. What happens debris collects in the blower box and clogs the drain. First sign is water swishing back and forth when you turn a corner, THEN. The wet carpet. Only thing to do is go to the dealer and have them clean it out and do it every year or you will have the same problem again.