Continuity mistake: The age gap between Eric and Cory decreases as the series progresses. At the start of the show, Cory is in 6th grade and Eric is a high school sophomore, meaning they are four years apart, give or take a few months. By season 3, Cory is in 9th grade (confirmed by dialogue mentioning that Shawn, who is in the same grade as Cory, is 15 years old), and Eric is a senior, leading to an age gap of three years. The first episode of season 4 takes place a couple months after the end of season 3, with Eric and Cory returning from a summer Road Trip, but just two episodes later, Cory mentions that he is in 11th grade, while Eric is still barely out of high school, leading to an age gap of two years.
Character mistake: When Cory is telling Shawn that he has a lot of questions about The Centre, Shawn invites him to check it out sometime. A couple scenes later when Cory does just that, an incredulous and defensive Shawn asks him why he is there, as if he forgot he invited Cory to check the place out.
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.
Factual error: When Shawn has first infiltrated the college philosophy class, the professor begins to resume the class' previous lesson on what he calls "Buridan's paradox," relating a dog caught equidistant between two bowls of food. This paradox in real life is known as "Buridan's ass," and as the name would suggest, concerns a donkey. While the name was probably changed to sound more family friendly, a college philosophy professor would certainly know the proper name and details of said paradox.
I Ain't Gonna Spray Lettuce No More - S4-E3
Continuity mistake: At the beginning of this episode, Cory asks Alan for money for his class photo. When Alan asks what grade Cory is in now, Cory says 11th. However, at the end of the previous season, Cory had just finished 9th grade (he and Shawn are both 15) and he spent his summer traveling the country with Eric. He should be in 10th grade, not 11th. This is further complicated later in the season, when he turns 16 and gets his driver's license. If he was in 11th grade, he would have already turned 16 and gone through driver's ed.
Other mistake: A lot of times in scenes in episodes taking place in high school, characters are shown walking up to their lockers and opening them without putting in the combination first.
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)
Answer: Topanga's middle name is never specified. Considering her sister's name is Nebula Stop-the-war Lawrence, Topanga's is probably something equally unusual.