Ward's offer to help Wally pay for the high cost of automobile insurance hinges on several conditions, including the concerned dad having final say on the excited, but naive, teen's choice of used car.
Beaver wins a 14K gold locket at the carnival ring toss and gives it to his friend Donna, after putting a picture of each of them inside; but Donna's angry dad won't let her keep the expensive gift and mails it back to Beaver without a note of explanation. Confusion reigns when June finds the locket hidden in Beaver's dresser drawer and thinks Donna gave the gift to Beaver.
After Ward reprimands him for being rude and inconsiderate, Beaver tries to do a good deed for Jeff, a hungry hobo with a hard luck story, who knocks on the Cleavers' kitchen door while Ward and June are out. Jeff convinces Beaver to make him a sandwich and let him take a bath but Beaver finds himself in hot water when his wily guest sneaks out of the house in one of Ward's good suits leaving a pile of dirty clothes for June to find when she comes home.
Showing off his new credit card, Eddie Haskell foots the bill for a new battery when Wally's car breaks down on the way home from a school function. Wally pays Eddie the cash to cover the charge but Eddie spends the money instead of giving it to his father and both boys are in trouble when George Haskell calls Ward to complain about the unpaid credit card bill.
Beaver's classmates and family plan to watch him "live" when he is chosen to appear as a panelist on the popular TV show "Teen Age Forum". But when everyone, including Beaver, misses an announcement that his episode will be taped for airing the following week, no one believes Beaver was really on the show...not even Beaver himself!
When Wally is notified that the State College scholarship he applied for went to Lumpy Rutherford instead, he graciously throws a party to celebrate with his friend and secretly helps out after Lumpy gets disappointing news.
Sulking because June made him do an errand for her instead of letting him help Wally and Eddie install a radio in Eddie's car, Beaver only speaks to her when necessary and starts playing up to his dad.
June isn't sure it's a good idea when eccentric Uncle Billy comes to stay with the boys while she and Ward spend the week-end at the lake with friends. But when Beaver is caught trying to sneak his friend Gilbert through the back door of the movie theater, he's glad that it's his good-natured uncle who gets the call from the theater manager and not his parents.
As grammar school graduation approaches, Beaver is torn between accepting Aunt Martha's offer to send him to a prestigious prep school in faraway New England or going on to Mayfield high school with the rest of his friends.
Ward is happy to write a letter of recommendation to his old fraternity, Alpha Kappa, when Wally decides to attend his dad's alma mater, State College; but Wally finds himself in a real dilemma when he's told that Alpha Kappa has a bad reputation and even Eddie Haskell doesn't want to join it.
Best friend Eddie gets jealous and girlfriend Julie thinks the worst when Wally innocently agrees to be the model for a sweater that Eddie's girlfriend, Cindy, is secretly knitting for Eddie's birthday.
Daunted by the length of "The Three Musketeers" that he chose to read for a school book report, Beaver writes his report from a film version of the story (The Three Musketeers (1939)) instead, not realizing until too late that the film that he watched was a musical farce.
Ward's dilemma over which son to take to a major league baseball game after he's only given two tickets seems solved when Beaver decides to go with Gilbert to the movies...until Gilbert's parents take him with them on a trip and Beaver tells his dad that he can go to the game after all.
When Eddie Haskell's uncle gets his nephew a summer job on a commercial fishing boat in Alaska, Eddie makes it sound so exciting that Wally and Lumpy want to go too...until Eddie's interview with the boat's captain bursts everyone's bubble.
After Lumpy Rutherford puts exploding smoke bombs in Wally's and Eddie's cars, Eddie coaxes Wally into retaliating against Lumpy with their own practical joke. But real damage is done to Lumpy's car when the joke goes wrong and Wally doesn't know that evidence left at the scene will lead the Rutherfords straight to the Cleavers.
Wally gets his parents permission to attend his all-night high school graduation party but finds that, if he wants to take his new girlfriend with him, he must make a good impression on her father who thinks all teenage boys are reckless and irresponsible.
June sends Ward to the principal's office to explain to Mrs. Rayburn how three of his good suits got mixed in with the old clothing donation that won Beaver the grammar school's "Good Citizen" award...and tell her that he wants them back!