The song playing right before Bart gets mud all over Nelson is "Metal on Metal" by Canadian heavy metal band Anvil.
This episode's title is similar to another Simpson episode: Homer Simpson, This Is Your Wife.
Running Gag:Homer pretending to be a magician, as he tells Marge that if she looks in her purse she will find the seven of clubs and then planting the seven of clubs in Marge's purse (Homer fails though, as Marge noticed him planting the card) and possibly Lisa's lunchbox.
Homer tells Lisa that he ate a slice of wedding cake Marge was keeping in the freezer (much to Marge's rage). There was also a slice of wedding cake in the freezer that Marge showed Homer in Natural Born Kissers.
When Lisa says that if she attends Cloisters Academy, she will make her old self look like Bart, leading Homer to respond "That'll be one weird kid." This is a reference to Lisa being a female version of Bart in the Tracey Ullman shorts and in the earliest episodes.