Deliberate mistake: Shawn fishes Mr. Feeny's watch from the septic tank and mentions the septic tank is deeper than it looked. Given this, he should be covered in human waste, instead of just looking a little dirty.
The Last Temptation of Cory - S3-E9
Deliberate mistake: When Cory calls Topanga from Missy's phone, he starts having a conversation with her as soon as he finishes dialing her number, with no time for the lines to connect.
Deliberate mistake: When Alan is trying to rush Amy out of the door, she yells from upstairs that she's still shaving her legs. A mere 20 seconds later, she comes downstairs wearing a dress and nylons. Even if she was for some reason shaving her legs while wearing a cocktail dress, that still wouldn't be enough time for her to clean off her legs, put nylons on and then walk downstairs.
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.