Character mistake: At one point Cory is telling Shawn about how he can't protect Topanga and they've only been married for one week. But they spent their wedding night in jail, 12 days on their honeymoon and 1 night in their new apartment. So actually the couple have been married for 2 weeks.
Factual error: When Cory and Topanga first enter their new couples dorm, they discover it to be a dump. The entire dorm is filthy, cabinets are falling apart, there are large bugs crawling on the floor, and there is no clean running water. Student housing laws would require the university to restore the dorm to liveable conditions before any student could move in. If the health department saw the conditions of the room, the university would undoubtedly be fined for failing to take corrective action. (00:07:45 - 00:10:36)
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.