Ward and June find themselves in the dark when they hear through the grapevine that not only is Wally going steady with Evelyn Boothby but that wedding bells may be heard soon. Meanwhile, Wally gets a different picture of marital life through Evelyn's sister and her husband.

June, Ward and Wally are going out for the evening and not wanting to worry about Beaver, June calls a babysitter, despite Beaver's pleas against the idea.

For $25, Wally buys a car and signs a contract with the owner knowing full well what he's getting, a car that doesn't start. Wally quickly finds himself with more trouble then he bargained for when the lemon becomes a fixture in front of the Cleaver home.

Beaver has told his parents that he doesn't want anything big for his birthday and they decide to respect his wishes and give him a gift of money. Beaver also gets quite a bit of money from other relatives and finds himself debating on whether or not to spend it or put in the bank, like his parents suggest.

A strange cat appears at the Cleaver's door and Beaver takes it in and feeds it. However, when the owner is found, and the cat is returned, Beaver finds himself with a dilemma. The cat keeps coming back.

Wally gets a job at the ice cream parlor leaving a gaggle of girls swooning and Eddie and Lumpy feeling neglected. So to get back at him, Eddie and Lumpy concoct a plan of revenge that involves Mary Ellen Roger's slumber party.

When Beaver and Gilbert are pretending to go for a drive in Ward's car, Beaver accidentally releases the parking brake, causing the car to roll down the driveway and into the street, backing up traffic. Wally steps in and drives the car back in the driveway and clears up the traffic mess, but he soon finds himself being issued a citation for driving without a license.

Wally's school is having an exchange dance and Wally and Eddie must take girls from a rival school that they chose out of a hat. Eddie asks to trade with Wally and he agrees, like a shot, after seeing the picture of Eddie's intended in a yearbook. Suspicious, Wally soon quickly discovers why Eddie wanted to trade; the girl is a few inches taller than Wally.

Beaver wants a new pair of expensive ice skates and asks Ward to borrow $13.00. Wanting to pick them out himself, he goes to the store and is conned by a salesman who sells him skates that her 3 sizes too big.

Wally and a bunch of other guys are invited to spend the weekend at Scott's cottage on the lake. However, the one thing that could keep Wally from going, Scott just happens to forget to mention, that there will be no parent supervision.

Beaver has been having trouble in English and Ward persuades Wally to tutor him. Wally has Beaver look over an old exam that he once took and to Beaver's surprise, the next day, his teacher gives him the exact same test, which he of course he aces. However, Beaver is left with a guilty conscience.

Wally plans on going to a big dance with Evelyn Boothby and they plan on getting there cramped with six other people in Lumpy's car. When June and Ward refuse to allow that, Wally and Evelyn must find another way to get there. However, what Evelyn has in mind doesn't go over well with Wally.

A party is being thrown at the dancing school where Beaver and Wally once took lessons and they're both invited. This prompts Beaver to ask one particular girl who caught his eye, Betsy Patterson, if he could escort her to the dance. However, once at the dance, he finds that Betsy has promised other boys that she would dance with them.

During a particularly awful golf game, Ward happens to break his driver and decides it's not worth repairing it, so he just puts it in the closet. Later, Gilbert talks Beaver into hitting around some golf balls with Ward's clubs and one hit with the broken driver has Beaver thinking he broke it.

Beaver learns a girl he fights with is leaving town.

Beaver is cast as a rabbit for a school play and June has his costume all ready, complete with floppy ears and puffy tail. On the night of the play, Beaver needs to be at the school early and gets a ride with Lumpy and Wally in full costume, however, Lumpy's car breaks down and Beaver must walk the few blocks to the school to get there in time.

June runs across Beaver's old electric trains while cleaning and since he hasn't played with them in years, finds someone who will take them, with Beaver's consent. However, Beaver quickly re-discovers the fun he has with his old trains and wants to withdraw from the arrangement, even though, the new owners-to-be are expecting them.

Beaver has Gilbert over to spend the night but after they watch a gangster movie things get out of hand. A suspicious car has just pulled up to the front of the house with two strange characters sitting inside, and they just happen to be Lumpy and Bill, dressed for a masquerade party. Not knowing this, Beaver calls the police and Lumpy and Bill are arrested.

Richard has just gotten, as Beaver describes it, a ""keen"" new jacket and this prompts Beaver to ask his parents for one exactly like it. June and Ward are hesitant after learning the price of one but decide to give in. However, when Richard loses his, he coerces Beaver into a plot to trick his parents.

Beaver becomes convinced that he's ugly and unwanted after constantly being reminded how cute he used to be and from being yelled at from his parents at how messy he currently is.

Wally is rounding up some guys to go to an amusement park and he's one short from getting a discount so he settles on Beaver. However, Beaver begins having second thoughts when he hears stories about one of the rollercoasters.

Beaver, Gilbert and Richard find a burro for sale in Mayfield and they each decide to each go in $10 for it. After getting their parent's permission, Richard and Gilbert fight over who gets to keep the burro, which they name Pepe. However, once they get a load of just how destructive a burro can be, they dump the problem of room and board on Beaver.

Eddie pompously announces that he's dropping out of school to get a high paying job at a gas station. However, all is not as it seems when Wally and Lumpy get a glance at Eddie's new free spending life.

A communication gap ensues when Wally wants to spend the night at Lumpy's and Beaver wants to have Gilbert spend the night. Beaver asks June and she tells him, he can sometime when Wally spends the night somewhere and Wally asks Ward, who tells him he can sometime when Beaver has someone spend the night.

Beaver agrees to help Richard cart his family's clothes down to the laundromat, however, half way there they discover that Richard has lost the three dollars his mother gave him. This leads him to ask Beaver if he could use the Cleaver washer. They soon find themselves in another jam when the washing machine overflows after Beaver put in too much soap and starch.