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: Igor's face is not disfigured on New Year's eve 1933, when he looks out at the crowd. The next scene in the morgue he is disfigured.