Judge Harm tells Homer not to spit on her cupcake and call it icing. This is a reference to Judge Judy (1996).
First appearance of Judge Harm, not to be confused with the female judge from earlier seasons voiced by Maude's former voice actresses Maggie Roswell.
The title is a parody of the 1998 Disney film "The Parent Trap" or possibly the 1961 Disney film "The Parent Trap."
Bart's chalkboard gag: Nobody reads these anymore.