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.
Continuity mistake: As Professor Wagstaff starts to address the students, he sees that Connie Bailey is sitting on the lap of his son, Frank. He asks her to stand up so he can see "the son rise." She stands up, but in the next scene she is back on Frank's lap and Frank waves and says, "Hello, old-timer!"