Continuity mistake: When the two men talk in the tent at the beginning, watch when one turns around - there is a clear cut in mid action where the men's positions change without any movement. (00:13:05)
Continuity mistake: When Chico and Harpo bring Groucho ice in his office at Huxley College, Harpo is wearing some kind of earmuffs. Between shots they change from going round his chin to behind his head.
Continuity mistake: When Harold climbs in the window of his house, his car rolls away to the right. After hearing the crash, he runs back to the window and looks out - to the right, where he sees the wreck. But that's the wrong direction. From inside the house, the wreck should be to the left. (00:08:00)
Continuity mistake: When Arthur Houseman takes out the water from the jug and replaces it with gin, you can see there are two glasses in front of the jug, but when we see him pouring gin into the jug in the next shot, the glasses have changed position.