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.
Audio problem: When Mr. Feeny is reading off the names of all the graduates, you can hear reverb in his voice to indicate that he is speaking into a microphone. The problem is there is no microphone in front of him. You can see Eric holding the microphone next to him and singing into it, with no audio. If that microphone is turned off, then Feeny's voice should not be amplified. If the microphone is on, then we should also hear Eric as he is singing. (00:19:38 - 00:20:56)
Factual error: When Topanga and Ricky are looking at the Starry Night painting, Topanga reads from her pamphlet and says it mentions Vincent Van Gogh became religious around the time he painted it. Van Gogh grew up in a religious household, with his father being a minister of the Dutch Reformed Church, and Vincent himself actually had a desire to become a pastor. On the contrary, however, when he painted Starry Night, although he still believed in an afterlife, he was actually disillusioned with religion.
Continuity mistake: When Shawn is grilling Kenny about asking to borrow Topanga's pencil, sometimes there is a female student sitting directly behind Angela with an open book on her desk, and other times the desk is unoccupied altogether. (00:00:21 - 00:02:40)
Continuity mistake: When Cory is saying to Lauren "Well, today I guess you're stuck with me," he slightly raises his left hand and then sets it back down on his left knee. When the shot changes, his left hand is suddenly resting on the couch cushion between his legs. (00:05:03)