Cory's Alternative Friends - S1-E4
Continuity mistake: Shawn claims his "sister, Stacey" uses the straightening stuff all the time. This is the only mention of her ever during the entire run of the show; and when Jack joins the show he is established as Shawn's only sibling.
Cory's Alternative Friends - S1-E4
Revealing mistake: While Cory and Topanga are handcuffed together, trying to convince their classmates to sign a petition to keep Mrs. Rosemeade, Cory is seen mouthing the lines the others are saying while waiting to say his own.
Grandma Was a Rolling Stone - S1-E7
Revealing mistake: When Eric first meets Mr. Feeny's niece, he throws a bag of mulch. When the mulch lands, you can see the fake grass move, and the fake background swings a little bit.
Revealing mistake: When Cory writes "Hey Dude" on the chalkboard, you can see how it had been written and erased several times, indicating previous takes.
Continuity mistake: When Mr. Feeny says "As if you are returning for your 20th high school reunion", there is a red crown on Mr. Feeny's desk with Minkus sitting on a chair at the end. After the camera cuts to a close up of Minkus saying 'More like a pre-union", there is a cut to Mr Feeny who turns to him. Minkus is all of a sudden holding the crown on his lap, then he is seen putting the crown back onto the desk. (00:04:00)
Visible crew/equipment: After Mr. Feeny says "You are the graduating class of the year 2000," he turns around in front of the back wall. As he turns around, there is a shadow of possibly a boom mic on the back wall which moves as Mr. Feeny moves. (00:04:15)
Santa's Little Helper - S1-E10
Visible crew/equipment: After the bell rings and Mr Feeny says "Have a wonderful vacation," a boom mic can be seen dropping from the top left of the screen as the students are rushing out of the classroom. (00:17:20)
Santa's Little Helper - S1-E10
Audio problem: When Amy is playing the piano with Morgan, the last few notes that they play while the camera is focused on them are out of sync. (00:19:50)
Plot hole: After Shawn leaves Cory's house to get a pizza, he calls Cory on the phone literally a minute later to tell him that Lenny Dykstra is at the pizza place. There's no way Shawn could have left Cory's house, walked to the pizza place, spotted Dykstra and either asked to use the restaurant's phone or found a pay phone to call Cory in such a short amount of time. (00:13:30 - 00:14:45)
Deliberate mistake: Morgan turns on the stereo and starts dancing on the sofa with her doll. She then tosses her doll, which tips over a plant and breaks the glass on a set of French doors. The stereo magically stops the moment the glass breaks.
Continuity mistake: When Cory is getting food for Shawn, he's piling meat loaf onto his plate. There are three pieces, one on top of the other two, then they cut to a wide shot and back to a close up of Cory, and it's just one larger piece.
Continuity mistake: When Alan is talking to Cory in his room, telling him that he can always come home, he is pointing his finger at him. He has his right arm rested on his legs and is pointing with the left arm. Just before the shot changes to face Cory, Alan stops pointing. In the next shot, facing Cory, Alan has his left arm resting, and is pointing with his right arm.
It's a Wonderful Night - S1-E18
Other mistake: When Eric is ordered to go to his room he mentions that Feeny used to be his 6th grade teacher. However, later in the series it is emphasized several times that Mr. Feeny was Cory's teacher every grade he was ever in. With Cory only being 3 years younger than Eric, it would not be possible for Feeny to have been Eric's 6th grade teacher as Cory would have been in 3rd grade and had Feeny as a teacher per what is stressed on multiple occasions later in the series.
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.