I had the same problem with my 300SD on the driver's door and did what I used to do with other cars: bend the metal rod.
Since there is some play in the metal rod, bending it effectively "shortens" the rod (straight line distance from end to end is now shorter) and removes the play. I noticed that MB lock rods are VERY strong. You'll need two strong sets of pliers. Hold w/one and bend with the other. Don't overdo it or the latch will remain partially "open". Just bend enough to remove the play. Mine door rattled all the time until I finally bent the rod and fixed it.
I believe Ford actually recommends this as a fix in their Explorer service manual (that's where I learned it..)
Neal Bhatt - email@example.com
'83 300SD 190k