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.
Other mistake: When Harpo and Chico are shooting spitwads at Groucho in the classroom, Groucho's line gets cut short when he is hit flat on the side of the head with a book. He then falls back and says, "You got me" and if you listen closely you can hear someone laugh in the background.
Continuity mistake: Groucho plays 'Everyone Says I Love You' in a boat, and he is playing a solid-body acoustic/electric guitar. At the end of the song, he throws the guitar into the pond, but it has become a regular hollow-body acoustic.