When I moved into this place one of the first things I did was shave down the top of the door to the furnace closet, as it was jamming against the frame due to the house settling at some time in the past. Not a big deal. However this resulted in the door now not staying closed because the latch was also misaligned with the striker plate due to the same shifting.
So, naturally, I went in and fixed it by shifting the striker plate up a little.
I also sanded off roughly 50 years of tarnish, scuffs, and sloppy paint, then sprayed it with a fresh clear coat. I'm happy to report that the door now closes perfectly and latches securely.
That's not to say this is the last time I'll be touching this door, however, as I still need to spackle in a bit of wood filler around the striker plate, and I'd also like to change out the doorknob for a paddle style that matches the other knobs in the house. Most of the knobs were replaced at some point with some lovely brushed nickel ones, but for one reason or another this particular door was skipped.