It has to be an older episode of the show. In the beginning in the part that shows the credits and gives the title of the show and producers and all of that you see Cory "run/jump" down the stairs and run out the door. You can clearly see that he DOESN'T shut the door. Then, he hops into the convertible with Topanga, Shawn, and Eric and if you look at the house you can see that the door is closed.