When entering the red door (turbo lift?) from the bridge, a video starts with the Interplay logo, but then the program ends (crashes?). The video is supposed to be " A Making of Star Trek: Judgement Rites video documentary presented by Leonard Nimoy."
The other videos (interactive interviews with Roddenberry and Nimoy) seem to work well.

Are you sure? The README.TXT on the Collector's Disk says "To quit the program, walk over to the lift doors and exit the bridge." So if that's the door you're using, it's probably working as intended. (When I do, I see a dedication plaque, followed by the Interplay logo, and then it ends.)

But I haven't really taken the time to look much at that bonus disk yet...

There is a bunch of videos that you can watch from the captain's chair, if that's what you mean. Or were there others?

Didn't get to the captain's chair yet. :-o
The ones I found are at the science officer's station (Spock's) right from the captain's chair, and on the opposite side.