Revealing mistake: In the last third of the film just after the announcement that Kong is coming, a native jumps out of his hut, loses his balance and falls by a chicken coop. His wig comes off and gets caught on the fence.
Continuity mistake: In the gala scene, Zeppo explains that Groucho is always on time and will arrive at exactly ten o'clock. Everyone starts singing the first big musical number, "When the Clock on the Wall Strikes Ten." There is even a shot of a clock set to ten. In the middle of the song, the clock strikes... six.
Revealing mistake: When the woman at the bar brings Jack the mustard which she forgot, Jack puts his napkin in front of his mouth. A fraction of a second before that, you can see the down-side of his face which should be invisible. Instead of nothingness you see it's all black. That is material used for the special effects, but they didn't 'make it invisible'. (00:06:50)