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Continuity: 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: Harpo Marx (made up like Groucho), breaks a huge mirror, with glass shards falling everywhere. This sets up the sequence where Harpo pretends to be Groucho's mirror image. The shards of glass have magically disappeared from the floor. The brothers are both in stocking feet-so their feet would have been cut up. It also would have been very noisy with the glass still on the floor. It's also interesting to note that the huge mirror has a room behind it - was it hanging in mid air?