When Maggie does better than Lisa on an IQ test, Lisa becomes so despondent over no longer being the smart one that she tries to change her identity.
Always Someone Better: Maggie to Lisa. Later subverted when it turns out Maggie only appeared smarter because of clues and hints Lisa was giving her. Double subverted when Maggie starts playing the saxophone.
Marge: All of my children are smart. Some are just smarter than the others. (Bart smiles ominously and puts his hand on Lisa's shoulder.) Bart: Welcome to the others! (Lisa screams.)
Eureka Moment: After Homer gets Phonic Frog to say "This is Huh-Oh-Muh-Eh-Er's doctor. He's too sick to work today", Homer momentarily laughs before he pauses in consideration and slyly excuses himself, no doubt to call Mr. Burns with the Phonic Frog.
Failure Montage: After Lisa's first two attempts at creating a new identity, we get a montage set to "Who's That Girl?" by Eurythmics... only to come to an abrupt end when Lisa gives up on the idea three attempts into the mont
Police Are Useless: When Homer and Marge report that Lisa is missing Chief Wiggum's response is to give them a form about police effectiveness, when Marge writes (generously) "somewhat satisfied" he implies he won't look for Lisa, when she changes it, satisfied, he takes Lou and Eddie out for smoothies, they spend the rest of the episode looking at optical illusions.