Continuity mistake: When Topanga is in the elevator and is saying "We'll just have to let nature take its..." the elevator door completely closes before she can say "course." When the shot changes to Cory saying "Nature take its what?", the door can be seen sliding closed again.
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.
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.
Factual error: This episode takes place near and on Christmas, but an establishing shot of the Matthews' house early in the episode shows the trees to still have very green leaves, and outdoor plants and the front lawn are still alive and healthy looking. None of this is possible in winter in Philadelphia.
Continuity mistake: When Shawn is talking about how the time Cory beat up his dad will be a great memory, the half of a cracker he is eating suddenly has another half-sized bite taken out of it and his hand is near his mouth. When the shot changes, the cracker is half-sized again and his hand is several inches away from his face. (00:03:40)