Eddie tells Wally that he is "going steady" with pretty Caroline Shuster. Is this like the time in the second season where Eddie said he "had a girl" but it turned out the two of them hadn't even met? No, she knows him, she calls him "Peachy" and she even fixes her hair he way that he likes. Wally and Eddie join Caroline and her friend at the soda shop where Eddie and Caroline make plans to see a movie that night. Everything looks above board to Wally, except for Wally having to ultimately pay for the tab that Eddie picked up for Caroline and her friend.
Later, Wally is picking up some photos he had developed at the drugstore, and Caroline and her friends are in the soda fountain booth nearby, and they have not seen him. There Caroline tells her friends that Eddie is a creep, but that her regular boyfriend is grounded for two weeks so she needs somebody to take her out. This upsets Wally, but he says nothing until he gets home and talks to Ward about what he should do - Leave it alone or tell Eddie. Neither option sits well with Wally. It does appear that Eddie has met his match in Caroline - She is someone willing to use somebody else to get her own way.
June spends most of the episode worried that Wally will follow Eddie's lead and want to go steady too.
At the end, Eddie has a candid moment with Beaver. And yet he usually treats the kid so badly, or at least is free with very bad advice. Eddie comes across as a guy who badly wants to be loved but whose father's affection is transactional. If he can't be loved then he'll be the center of attention by being a wise guy, acting like nobody actually matters to him, when in fact they do.