Why do my '64 Continental suicide doors keep sticking at the back corner?

Body mounts whould be pretty far down my list. If the floor pans have rust in the rear areas, the mounts themselves could be compromised, and that's worth fixing eventually, but a subtle body shift rarely causes one corner to hang like that while the fronts are fine. Hinge wear and swollen weatherstrip cover the vast majority of these cases. Slamming it harder is the one thing to avoid since a bent striker or latch just makes everythign harder to diagnose.

Had the same hang-up on the rear corners of an old car I did, turned out the hinge pins were shot and the door was drooping just enough that the roller couldn't seat in the striker. Grab the door at the outer edge and try lifting it. If it moves up and down much, that's your answer. New pins and bushings are cheap and a weekend job with a helper holding the door. While it's off, I cleaned the latches out with brake cleaner and some light oil, and mine caught way crisper afterward. Do the lift test before you buy anything.

Before you buy anything, mark the striker with some soap or chalk and close the door slow a few times. You'll see exactly where the roller's hitting, wheather it's catching high, low, or short. On my old Caddy the striker bolts had loosened just enugh that it sat a hair low and nothing lined up, no parts needed, just loosened and nudged it. Takes ten minutes and tells you a lot. Also, don't over-oil that latch, too much grease in there just gums up the spring and makes it feel worn when it isn't.

On these suicide doors the bottom corner swings a longer arc than a regular door, so a hair of misalignment shows up big down there. I had a '62 that did the same thing and it was the hinge kicked out at the bottom, not drooping. Loosen the hinge bolts enough to wiggle and shift the bottom of the door in a hair, then try it. An old bodyman I worked with used a two-by and a floor jack under the door edge to nudge things around before final tightening. Also check the latch springs, on those old Fords the return spring goes soft and the pawl stops pulling all the way even when everything else is fine.

This thread is teaching me a lot since I've got an old sedan with doors that need a good hip-check to shut. Curious about the rust thing though, if the floor is soft back there, does the door frame itself bend out of shape over time? My uncle had a car where the whole opening looked kind of twisted but he never figured out why. Would a frame problem show up the same way as a loose hinge, or does the gap around the door look uneven too?