rattlepaneltrim
The short answer is that it is an easy fix...the whole answer is that unfortunately, to do it right, you must remove door hardware, and the panel from the door...The small chrome trim has a section like an almost closed staple, and this channel section holds within it, (often loosely, in your case..)a pronged molding...and the prongs, every 3" or so, go through a respective hole in the door card (the pressed board panel that your vinyl covering goes over) and then bends against itself to secure the small chrome trim...like a metal closure on a large mailing envelope. Over time, the holes in the pressed board will enlarge/ream out so that the prongs can move, as yours does, from front to back....
SO...if you need to clean your window motors, or other interior door job, its a good time to check out your door cards...and possibly make new ones from the proper thickness of plywood if yours are soft from time/moisture. (note:too thick, and the vinyl will not re-install properly, too thin, and the staples will shoot through...and the plastic thingies that hold the panel to the metal door frame wont attach properly..does it sound like I have travelled both wrong roads before...?) If your door cards are ok, and the rattle is just the pronged molding moving within the chrome trim, then you need to JB Weld the molding to the inside of the chrome trim after the above removal of the door cards...For door card removal instructions, check the e9 site archives as I think I remember seeing the how-to...
Easier temporary fix might be to cut couple of small sections of rubber band (or better, booger glue from a magazine insert...you know, the stringy stuff..) and work it behind the chrome trim in a couple of places with as not-sharp, thin scraper or spatula, to serve as a pressure "gasket" to keep the rattle down to a whisper...
I doubt that any of this is in the bmw blue book manuals...good luck.
Dave V. in NC