Continuity mistake: If you look in most of the scenes, especially the one where she is throwing the stuff out the window, you can see a wall out of the window, but in the scene where Cory comes back from seeing the lady you can see a dresser out the window.
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.
Continuity mistake: When Cory is whispering in Amy's ear, she is holding a cup of frozen yogurt in her left hand. When the shot changes, she is holding it in her right hand. (00:16:40)
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.