Other mistake: When Eric asks Mr. Williams why everyone is applauding Frankie missing a shot in their game of pool, Mr. Williams notes it's because no-one has ever seen two people play for three hours without sinking a shot. However, if you rewatch a couple of times the part where Frankie takes his shot and you count the balls on the table, there are only 14, not including the cue ball, when there should be fifteen. If by chance a ball was knocked off the table, then given how much the crowd was into the game, someone would have told them they needed to place the ball back on the table.
The Heart is a Lonely Hunter - S3-E15
Other mistake: Dana exits Chubbie's and sees Shawn has set up a picnic for her. She remarks that it's the middle of winter and Shawn is shaking from the cold, but her breath is not visible.
The Pink Flamingo Kid - S3-E17
Other mistake: When Eddie busts Cory filming him and his cronies, he spends a few moments intimidating Cory before snatching the camera out of his hands and throwing it against the ground. After Shawn breaks up the situation and notes that they broke the camera, Cory remarks that they didn't get the tape and proceeds to pull a tape from under his jacket. Cory's hands are both visible gripping the camera the entire time that Eddie is confronting him, and he didn't have the opportunity to retrieve the tape when Shawn intervened, so he couldn't have had the tape tucked away.
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.