Sorry to necrobump this thread but I just had this problem happen to me last night. I was lucky and noticed the driver-side window down so I was able to roll that one up but the passenger-side window was *also* down and I didn't notice it. This morning I got up to see that rain had gotten in on that side. Want to see what it did to the leatherette armrest?
EDIT: Found out that since both windows were down it was probably due to me pressing and holding the unlock button accidentally. For all those who don't know about that "feature": beware! BMW of Austin referred me to Devine Color to get the armrest refinished.