No, it just has all the pins attached along the edges of the panel.
They're sort of crimped on, then covered with a clear layer of what
appears to be some type of hard conformal coating. I've noticed that
sometimes I can get a bad segment to come on by tweaking the display a
little, but only while applying some force. It appears to be bad
connections, probably where the pins connect to the panel. The pins are
soldered into the PCB, so I know the problem's not there.


Bummer, sounds like your initial diagnosis of a bad display is definitly
correct, it'd be worth checking surplus places like All Electronics, HSC,
Alltronics, and a number of similar places.