Other mistake: When Cory and Shawn are auditioning for "Guys" and they're talking about the first person they pick, Cory says,"He's shorter than me and..." but after they pick both guys and he's talking to them, you can see that Cory is the shorter one.
Revealing mistake: When Cory and Shawn are holding band auditions, if you watch the guy that is shredding on guitar, you can see that although he is moving his fingers all over the fret board, his picking hand remains motionless, showing that he isn't actually playing and the sound was added in post production.
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.