Oldie but a Goodie!
I found my driver side middle floor damp a month ago and blamed my son for spilling his water bottle. A month later I happened to park outside one night and a HUGE storm came through. Couple days later I noticed a musty smell and the same area was wet again... and I wound up here reading through several similar threads.

The weird thing about my issue was that at first I thought it was something else... Looking at the bottom of the door - the hollow tubular rubber wind seal that runs around the door seemed to be weeping water out of the tiny holes punched into it at the bottom. (pic 1) I repeatedly squeezed the seal from either side toward the holes and several ounces of water squirted out. I could NOT figure out how the water would have gotten inside it, as the seal is in like new shape all around, and is not open or torn anywhere.

All the posts here pointed to the Vapor Barrier or the sunroof drains. I park inside exclusively so my drains are all very clean. That's when I noticed the dried up drip marks coming from under the door card, and sure enough when I pulled it off the Vapor Barrier was detached in a few spots. It would appear the water running from under the vapor barrier ran down to the wind seal and, having nowhere to go, must have filled it up via those little holes.

It just so happens this door was replaced a few years ago when someone backed into it and crushed it. You would think when they reassembled it and installed this barrier it would have outlasted the other 3 original doors.... But here we are.

I wanted to thoroughly dry the floor while I did the door repair, and what a pain it is to pull up the carpet. Had to remove the middle seat on that side, holy crap it weighs a ton. Then a bunch of trim to pull the carpet up enough to aim a heater under there to dry out that thick foam padding underneath. (pics 2-3) I tried to remove the B pillar trim for even better access but BMW fastening methods are just inscrutable most of the time and I gave up. But I let it dry all night like in the pic, seems fine now.

I have two kinds of Permatex in the garage to choose from - Black (heat resistant) and Blue. Either should be sufficient to seal this puppy up.
Now I am wondering if I should check the other doors, or just wait for more wetness.

*Another tip for others: For all the wiring connections to the back of the door card, I always spend 5 minutes cursing and trying to figure out how to press little tabs to get the connectors apart while holding the card up, until I just pull hard and they disconnect. Every one of them.

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2012 e70 X5 50i MSport "The Boss" black on black *Well Optioned*