Continuity mistake: When Gottlieb discovers Driftwood in his opera box and the latter escapes by climbing to another, Gottlieb leans against the wall and calls him a "Schweinhund." The shot then cuts to the orchestra, but the box (with Mrs. Claypool in it) is still visible and Gottlieb has somehow vanished.
Continuity mistake: In the contract scene towards the beginning, Groucho and Chico, after the second part, start tearing away subsequent parts without reading them aloud. They tear off one because Chico doesn't like it (the third), one because Groucho won't like it (the fourth), and two because Groucho's word is not good enough for Chico (the fifth and sixth). At this point they should be at the seventh part, but when Groucho reads again he begins with "the party of the eighth part..."