Singled Out - S4-E7
Continuity mistake: The same girls keep leaving the stage every time Eric answers a question.
Continuity mistake: When Cory first confronts Shawn over kissing Topanga in their dorm room, Shawn is looking through his drawer for a shirt. The shot goes to Cory for a second, then when it goes back to Shawn he's had time to find a shirt and put it on - the shot wasn't off him for nearly enough time to do that.
Revealing mistake: The firefighters, apparently the fastest men in the universe, appear no more than 10 seconds after the fire starts.
Stupidity: When Eric, dressed in drag, tearfully sits down next to Topanga, she asks him if they know each other because she doesn't realise it is him. Topanga's known Eric practically her entire life, and she is one of the smarter characters on the show. Given that Mr. Feeny instantly recognized that Eric and Jack were dressed up as women, Topanga should have recognized it immediately as well. (00:10:40)
Suggested correction: This is a comedy show and this scene is played for laughs. A character not recognizing another character in drag when it is obvious to the audience has been a joke for centuries. Also, on a realistic level, recognizing faces has nothing to do with intelligence.
There's a difference between not recognizing someone you might barely know and being fooled by an obvious disguise worn by someone you've known for 20 years. I fully acknowledge that this scene is played for laughs and that this is a common trope used in movies and television, but the fact that the show went out of its way to show that Mr. Feeny instantly saw through their disguises demonstrates that show itself acknowledged how ridiculous his disguise was, and it was foolish on Topanga's part for not seeing through it.
Janitor Dad - S4-E6
Deliberate mistake: Chet comes home from his first day as school janitor brandishing a paycheck, which impresses his wife and in turn changes Shawn's mind about Chet working at the school. Being that it was Chet's first day on the job, there's no way he would already have received a paycheck. Even if it was payday, his employment would have begun on the first day of the next pay period.
Suggested correction: It's possible it was pay for training or orientation days that were before his official start date.
Continuity mistake: In every other episode where Shawn's trailer is shown, next to the kitchen there was always sort of a hallway leading to bedrooms/bathrooms. When Shawn and Jack are in the trailer in this episode, there is one big wall.
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.