Check for play at the hinges. If the pins are worn or seized in the bar that attaches to the door (very common) the pins will wear into the cage that bolts to the door pillar. If the latch end of the door will move up and down when open, it's probably time to remove the hinges and check them out. My door hinges weren't too bad, as far as looseness, but when I remove the doors and hinges, the wear was revealed. I rebuilt them with new pins and drilled the bars attached to the doors for bronze bushings and used oversized hinge pins. I also replaced the faceplates on them as they were bent a bit at the margins from the door opening a bit too wide.
