And in Case I Don't See Ya - S6-E10
Continuity mistake: When Mr. Feeny is looking over Cory and Shawn's papers, he rests Shawn's paper on the plate with his omelet. When the shot changes, he is holding the paper in his left hand and it is raised away from the plate. (00:18:35)
And in Case I Don't See Ya - S6-E10
Continuity mistake: Rachel gets water poured on her and her pants are soaking wet. When she goes into the Student Union, Eric says "you got here incredibly fast." Her hair is still wet but her clothes are completely dry.
And in Case I Don't See Ya - S6-E10
Continuity mistake: When Cory, Shawn and Feeny are at the table, Feeny's glass is almost half full. Cory later fills it up, but in the next shot the glass is half full again. In a later shot it's full and then it's somewhere in between half full and filled up.
Chosen answer: In the present day, with the United States abiding by more stricter school health laws, for the most part this wouldn't be in school cafeterias as many cannot even have carbonated beverage machines now. However, in the 90s when the show takes place, it wasn't unheard of for there to be coffee machines in the cafeteria of small schools where the teachers eat with the students as we see them do often in the show. The idea being that the cafeteria was small enough so a teacher or hall monitor could catch a student before they could drink the coffee.