Easy Street - S4-E12
Continuity mistake: In this episode Alan says that Eric woke him up on his 16th birthday to get his driver's license and it's a tradition for the men of their family to go with their fathers and get their license, however in season 1 when Eric does get his license, he says that Amy and Alan let him go off with Jason to get his license and there was no celebration.
It's a Wonderful Night - S1-E18
Other mistake: When Eric is ordered to go to his room he mentions that Feeny used to be his 6th grade teacher. However, later in the series it is emphasized several times that Mr. Feeny was Cory's teacher every grade he was ever in. With Cory only being 3 years younger than Eric, it would not be possible for Feeny to have been Eric's 6th grade teacher as Cory would have been in 3rd grade and had Feeny as a teacher per what is stressed on multiple occasions later in the series.
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.
Deliberate mistake: Shawn fishes Mr. Feeny's watch from the septic tank and mentions the septic tank is deeper than it looked. Given this, he should be covered in human waste, instead of just looking a little dirty.
Visible crew/equipment: After Amy's C-section Alan walks into the waiting area, and just as his kids gather around him in the wide shot the boom mic dips into view at the top, center of the screen between Alan and the plant (viewed on iPad screen). (00:20:10)
Continuity mistake: When Cory is lying on the couch during his argument with Topanga, the pink pillow is under his right shoulder. A few shots later, it is suddenly under his neck. (00:17:00)
Continuity mistake: After Topanga and Angela hug, Angela puts her hands on Topanga's arms. When the shot changes, Angela's arms are suddenly down at her sides. (00:18:27)
Continuity mistake: When Topanga is telling Cory that she had her internship interviews in the morning, her arms are folded. When the shot changes, her arms are down at her sides. (00:07:39)
Continuity mistake: When Cory is saying to Shawn "Are you going to nice yourself out of the girl you love?", Shawn's right foot is resting on his left knee, and his left hand is on the foot. When the shot changes, his left foot is now resting on his right knee, and his left hand is resting on his left thigh. (00:05:06)
Continuity mistake: When Cory enters the noir world and uncovers Topanga's corpse, you can see her left hand is draped over her stomach. After the noir version of Cory confesses to the murder, the cloth covering her body is now suddenly covering more of her torso, including the left hand. (00:17:53 - 00:19:15)
Continuity mistake: When the noir version of Shawn is asking Topanga what she's running from, the pot of coffee is next to his left arm near the edge of his side of the bar, and the coffee mug is slightly to the left of the crease in the bartop. When the shot changes after she asks him what he means, the mug is now directly over the crease, and the pot is in the center of the bar between the two of them. (00:06:53)
Revealing mistake: When the noir version of Eric is talking about the noir version of Jack as he is playing the piano, you can see Jack is just tapping his fingers against the piano keys and not actually striking them. (00:05:33)
Continuity mistake: When Topanga gets sucked into the time continuum vortex, you can see a teddy bear between the skis and a pair of shoes. When the shot changes to Cory, you can see the skis and the pair of shoes, but the teddy bear is now missing. (00:04:03 - 00:04:33)
Continuity mistake: When Cory is telling Topanga that he wants to be sure Wile E. Coyote will be all right, you can see a single piece of popcorn on the right side of the microwave stand in the background. When the camera switches back to Cory after Topanga assures him he's always all right, the piece of popcorn is now gone. The amount of popcorn on Cory's shirt also decreases in both aforementioned shots. (00:02:15)
Continuity mistake: When Eric purchases Rachel's tank top, the placement of his right hand while holding it changes when he says "I'm a collector." (00:10:43)
How Cory and Topanga Got Their Groove Back - S7-E18
Continuity mistake: When Eric sneezes on Jack's cereal, Jack is holding the carton of milk level with his abdomen. When the shot changes, he has already set the carton down on the counter. (00:04:30)
How Cory and Topanga Got Their Groove Back - S7-E18
Continuity mistake: When Eric is saying to Jack "It was you all along," he points his left-hand index finger at Jack, who is shown writing down the lottery numbers Eric provided him. When the shot changes, Eric is now pointing with his right hand, and Jack's hands are suddenly on his hips. (00:16:40)
She's Having My Baby Back Ribs - S7-E17
Continuity mistake: When Alan remarks that Amy never got her figure back after she gave birth to Eric, her arms are folded. When the shot changes, her arms are down at her sides. (00:10:10)
She's Having My Baby Back Ribs - S7-E17
Continuity mistake: After Cory says "You don't have to tell me that" after Shawn compliments his waffles, Shawn is shown holding the fork pointed down towards the waffles. When the shot changes, he is suddenly holding holding the fork perpendicular to his body. (00:04:35)
She's Having My Baby Back Ribs - S7-E17
Continuity mistake: When Jack, Rachel and Angela start heading to their class, a shot of Topanga shows her holding a slice of pizza slightly raised from her plate. When the shot changes, she is suddenly holding the pizza several inches above the plate. (00:01:04)
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.