The arm rest is connected to the panel with plastic rivets from the inside. A couple of mine were broken so I just drilled the rivet partially (enough to make a 1/2 inch deep hole but not too far to puncture the arm rest skin) and used a 1/2 pan head screw to hold the thing together. It works well. This will be clear once you have the panel off.

The other source of rattling is possibly the window regulator. At the point that it's rattling you might consider replacing it. Not too hard at all once the door is apart. (many threads on the subject here) And more than likely to fail eventually since it gets used more than the other windows.

DS
87 300D
Northern Iowa