In the E39s (which I know, vs the E85/86 which I don't yet), the door vapor barriers go bad and let water in that way. Check under the bottom of the door and the seam where the door card meets the door itself and see if there's any moisture sloshing around in there. You might also check the carpet where it curves up toward the door. If it's wet there, that points to a door-based issue.
But that's the E39. Worth a shot, though.
