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.
Continuity mistake: After Jack strangles the police officer there are 3 guys by the door - he knocks down one of the them but in the next shot there is just one man left.
Continuity mistake: When Oliver's wife comes to see him in the dining room, you can see she is wearing frilly sleeves. But when she goes into the kitchen in the next shot, the sleeves have gone.
Continuity mistake: When Oliver gets stuck in the vent port, he has his arms tucked inside. When we see Stan climbing up a ladder to give him his bowler hat, Oliver has his arms outstretched.