A Long Walk To Pittsburgh (1) - S4-E16
Character mistake: After learning that Topanga will be moving to Pittsburgh, Cory tries to rationalize their desire to be together for the rest of their lives despite still being so young by comparing their relationship to that of Romeo and Juliet, thinking they turned out OK. Shortly thereafter, he is shown reading the book in his backyard and explains the situation to Mr. Feeny, who advises him to skip to the end to find out what happens to their relationship, much to Cory's dismay. The problem is that Cory already learned the fate of Romeo and Juliet in Mr. Feeny's class in the first episode of the series. He was even dismissive over the idea of a man killing himself over a woman.
A Long Walk To Pittsburgh (2) - S4-E17
Character mistake: In this episode Cory says that Topanga gave him his first kiss at age 13, but their first kiss actually happened when they were 11, in the 6th grade. (Season 1 - Episode 7 Cory's Alternative Friends).
Character mistake: When Cory is telling Shawn that he has a lot of questions about The Centre, Shawn invites him to check it out sometime. A couple scenes later when Cory does just that, an incredulous and defensive Shawn asks him why he is there, as if he forgot he invited Cory to check the place out.
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.