The Grass is Always Greener - S3-E12
Continuity mistake: Early in the episode when Cory is talking to Shawn by their lockers, Shawn closes his locker and you can see one of the straps from his backpack sticking out on the bottom-right side of the locker. A few shots later, the strap is now sticking out on the bottom-left side. About a minute later in the scene, just before Topanga comes to talk to Cory, you can see the strap is now sticking out of the bottom-middle area.
A Kiss is More Than a Kiss - S3-E14
Revealing mistake: When Cory puts the talking teddy bear that Topanga gave him in the trash compactor, the bear screams and Alan and Amy come down to investigate. Amy opens the trash compactor door and pulls out a bear crushed into a cube, but if you look closely, you can see the original bear still in the trash compactor unharmed.
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 Heart is a Lonely Hunter - S3-E15
Revealing mistake: When the news director is flipping through the booklet that is Arthur's résumé, you can see the pages are blank.
The Pink Flamingo Kid - S3-E17
Visible crew/equipment: After Amy says to Eric, "Whatever makes you and Kyle happy", the shot changes and a boom mic can be seen being pulled out of view on the left side of the screen.
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.
Revealing mistake: When Topanga emerges from the kitchen with more ice for Cory, instead of seeing the kitchen through the open doorway, you can see a wall with framed pictures, suggesting another set was there in place of the kitchen.
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.