Once the door panel is removed, there is a sheet of foam covering the inside of the door (it's a sheet of plastic on older models; BMW calls the foam "sound deadener"). It is glued on with a strip of tar-like substance. That substance is butyl tape. Often, it dries-out and fails at the bottom of the foam sheet, which allows water to run behind the door panel and into the car.
You mentioned that you know of a leak at the top, so you might not have a door leak.
Once you have the door opened, it's a perfect time to lubricate the window slider tracks as well. The plastic slides might need to be replaced. It might also be a good time to replace the seal behind the outside door handle, if yours is cracked. In my case, it was also time to replace the door speakers.