Rusty, With the door closed try pushing and pulling on the outside handle to see if it will move or rattle. Open the door and hold it by the outside edge to see if it moves up and down. Are there loose fasteners? The hinges, pins, dovetails, rubber, Latches or striker plate could be worn. Likely one or more of these need tightening replacing or repair.
New rubber, dovetails, striker plates, hinges and fasteners can be purchased from the dealers. Also available are oversized pins to repair hinges.
As far as the body I would consider the Model "A" passenger car flexible but "AA" trucks not so much.