A Long Walk To Pittsburgh (2) - S4-E17
Character mistake: In this episode Cory says that Topanga gave him his first kiss at age 13, but their first kiss actually happened when they were 11, in the 6th grade. (Season 1 - Episode 7 Cory's Alternative Friends).
Character mistake: At one point Cory is telling Shawn about how he can't protect Topanga and they've only been married for one week. But they spent their wedding night in jail, 12 days on their honeymoon and 1 night in their new apartment. So actually the couple have been married for 2 weeks.
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.
For Love and Apartments - S7-E2
Character mistake: When Shawn is scolding Topanga for getting angry with Cory for travelling to Pittsburgh to try to get her parents back together, he mentions that he travelled a hundred miles to do so. Philadelphia is roughly 300 miles from Pittsburgh. Travelling only 100 miles westward from Philadelphia would barely get them past Hershey. (00:17:53)
Better than Average Cory - S6-E5
Character mistake: The placard next to Alexandra Nechita's painting "Peace Collector" erroneously calls the painting "Peace Collectors." Nechita herself appears in this episode, so it's odd that they got it wrong. (00:02:49)
A Very Topanga Christmas - S5-E11
Character mistake: When Cory is talking to Alan in the middle of the night, he mentions that Topanga has been staying with them for less than 8 hours. She arrived during the day time, and then convinced the family to go to Vermont to get a real Christmas tree, which they are cutting down at nighttime, and Eric later expressing after the new tree has been put up and decorated that it was 600 miles round-trip. All of this would take more than 8 hours. Driving from Philadelphia to the southernmost part of Vermont and back again alone would take more than 8 hours.
A Long Walk To Pittsburgh (1) - S4-E16
Character mistake: After learning that Topanga will be moving to Pittsburgh, Cory tries to rationalize their desire to be together for the rest of their lives despite still being so young by comparing their relationship to that of Romeo and Juliet, thinking they turned out OK. Shortly thereafter, he is shown reading the book in his backyard and explains the situation to Mr. Feeny, who advises him to skip to the end to find out what happens to their relationship, much to Cory's dismay. The problem is that Cory already learned the fate of Romeo and Juliet in Mr. Feeny's class in the first episode of the series. He was even dismissive over the idea of a man killing himself over a woman.
Character mistake: After the production assistant walks away from the catering table, he walks into the area where the Matthews are being interviewed. Any production assistant would know better than to just casually walk right into the shot when a live televised interview is going on.
Character mistake: After Cory and Topanga have their argument in front of everyone, Cory remarks to Shawn that it's their first fight ever. Cory and Topanga had several fights in the show prior to this. (00:12:50)
Character mistake: When Sarah the waitress is filling up Cory and Shawn's coffee cups, she puts hardly any coffee in them, with Cory's barely being a couple of drips. A waitress that works on tips wouldn't be so lackadaisical about filling a customer's coffee cup. Cory and Shawn just sat down as well, so it's not like she was just topping them off. (00:02:58)
The Eskimo - S5-E13
Character mistake: In the opening scene, Cory remarks that they have been in high school for 4 years and there's nothing left for them to be taught. They began high school in 7th grade and are now midway through their senior year, so they have actually been in high school for 5 and a half years.
Suggested correction: There's a difference between being at the same school and being in high school. For most students, high school is 4-years long (9th-12th grade). When I was in kindergarten, I went to a K-12 school. If I graduated from that school, I wouldn't have said I was in high school for 13 years.
It's openly stated numerous times beginning with season 2 when they are in 7th grade that they are now in high school. The school is even called John Adams High School, and not something like John Adams K-12 or anything like that. I remember being baffled by this growing up, because high school for me did not begin until 9th grade, and even then, we didn't attend an actual high school until 10th grade. It may be unconventional compared to real life, but the show firmly established that they were in high school starting with 7th grade.