Graduation - S5-E24
Factual error: In the episode Class Pre-Union, they were the class of 2000. In the episode Graduation, they were the class of 1998.
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.
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.
The Eskimo - S5-E13
Factual error: When Shawn and all the other contestants - as well as the radio DJs and onlookers - are standing out in the cold for a chance to win Super Bowl tickets, no-one's breath is visible, nor are any parts of their faces red.
A Very Topanga Christmas - S5-E11
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.
Factual error: The Starry Night painting that characters look at in the Van Gogh exhibit is mentioned as being the original painting itself. However, if you compare the painting presented in this episode with the real-life painting that is displayed in the Museum of Modern Art, you can see that it is an imitation, as the colors are brighter and the little details in the painting are not as prominent.
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.