In several episodes, the names and identities of Topanga's parents change. In season one, she calls them Jedediah and Chloe. In later seasons, they are Jedediah and Rhiannon. In total, four men and three women have played Topanga's parents, including a casting change right in the middle of a story arc regarding their divorce.
At one point, Cory states that Mr. Feeney has been his teacher since first grade. However, in the first episode Eric tells Cory that he's going to have Mr. Feeney now that he's in sixth grade, suggesting that he did not have him in previous grades.
The way Cory and Topanga met, how old they were when they were met and how long they have been "together" changes numerous times throughout the series.
In the seventh grade hallway, the boys bathroom was also used as Mr. Feeny's office and as a guidance counselors office.
In the second season (Cory's first year of middle school), the locker right next to Mr. Turner's classroom changed ownership throughout the year. It was Frankie's, then Cory's, then Shawn's, and then Eric's. Every time it is shown, there are kids in it but it belongs to a different person.
Shawn is listed in the series as living in a trailer park in West Philadelphia. West Philadelphia has no trailer parks as it's known as the poor section of town. West Philadelphia is actually known for housing projects and section 8 housing and is predominately African American neighborhoods.
As with any long running series, certain details change as the show progresses and writers change. Both Shawn and Topanga, for instance, have sisters in the first season but are later depicted as only children. In the show's earlier years, Topanga's mom was named Chloe, but in later episodes she's known as Rhiannon. Inconsistencies like these are generally forgiven in series.
In the opening credits, the characters are driving on the wrong side of the road.
The beer cans that Shawn and the homeless bum drink out of in "If You Can't Be With the One That You Love" changes between shots. One shot is a can of Miller High Life, while the next shot is a can of Schlitz.
In "Sixteen Candles" both Shawn and Corey go back and forth between the Wrestling match at the Spectrum and to Topanga's birthday party. In actuality this isn't possible since Corey and Shawn would have been stuck in Philadelphia traffic and by the time they got back to the Spectrum, the wrestling matches would have already been over.
Near the end of "The B- Team of Life", When Amy is walking down the stairs saying that Morgan wants to hear a Story from Corey, There is a boom mic on the top of the screen right in front of the shelf to the right of the stairs.
Whenever flashback scenes show Cory as a young boy, the actors playing younger Cory are always right handed. Cory (as well as Ben Savage in real life) is really left handed.