While Professor Post (Buster Keaton) is dragged by the train, clutching his luggage, his hat flies off and he is unable to grab it. In the next shot, his hat is once again firmly on his head.
In the scene where Buster and Thelma get drunk, he gets undressed and goes into the bathroom. There's a cut to Thelma, then back to Buster, who's still in his underwear but soaking wet. The presumption is that he took a shower with his clothes on, but there's no such scene, nor has enough time has passed for him to have taken one. Evidently the scene was filmed but cut, and whoever did so just hoped no one would notice.
When Buster is loading his trunk, there is a table lamp on his desk. He grabs the large coat tree and places it in the trunk. There is a jump cut, and the coat tree has disappeared, while the butler pulls the lamp out of the trunk and puts it back on the desk. It would appear that two different takes of this scene were cobbled together.
When Professor Potts puts the girl that was on his shoulders down, he is not wearing his glasses, he then has his glasses back on when he addresses the crowd.
The sign for Potts College gives its founding date as "AD. MDCCCLXXVI." The proper abbreviation is "A.D." for "Anno Domini."