I have a soggy driver's side wet carpet as well. I'm replacing all the door seals on door and Jeep to hopefully fix the problem. I can actually see the water/rust stains on the area of the side of the dash when the door closes and rest next to it. It's not crazy, but enough to get wet over time. I hate the wet dog smell when I get in it. To assist in drying, let the Jeep run, put the A/C on high, but turn it to heat. It'll help pull the moisture out so you don't get mold/mildew.
98ZJ 5NINER-Trail Ready Front w/ Grill Guard--Rugged Ridge 8500lb-IRO 5 1/2"LA Fully Adj.Kit-16x8 Pro Comp 7089 Flat Black-35x12.5 Pro Comp Mudd Terrains--Upgraded to NP231HD-Tom Woods Rear Shaft-Rusty's Intake-K&N Filter--ADDCO F & R Sway bars, Currie HD Steering-3"Cat back w/ Flowmaster 50-TireGate HG Series Rear tire carrier