The door in question was affixed w/ screws that were 1/2" long. The ones on the bottom hinge had fallen out completely after just 9 years. The holes they left behind weren't rescrewable.
I went out and got some 1 1/2" screws, replaced all the wall-side screws with those on the failed door, and also replaced 1 screw on each hinge into the door. (Figuring that the door wood is going to be harder than the jam wood.)
Any reason why I wouldn't go through and do all the interior doors in the house this way? (Or some other way? Advice welcome.) I imagine that it's much better to do a repair like this before the screws start wiggling around and boring out holes in the door jam, but is there some advantage I'm missing to shallower screws that might make me want to leave well-enough alone?