I seem to recall Dave's picking up the banjo as "his" instrument, fairly late into the game. He picked up Pete Seegar's book and studied the hell out of it, even writing to Pete about technique. "Tom Dooley" might have been a song they developed prior to Dave's leaping into the 5 string. This is only a guess. Nick said that Dave was "a quick study", and he could pick up anything very rapidly, devoting a huge amount of time and using it well.
Regarding the film, I think this may be one of the earliest performances I've seen. Berle was television's king at one point, so if the act was "hot", Uncle Miltie was the place to go. Very historic and informative piece. The gus aren't as polished and secure in their live performance. Very early.