Sneaky Frankie Bennett tells Beaver that he can win a new bicycle by entering a popular television show's Franklin Milk bottle cap contest; but Beaver and big brother, Wally, cause quite a commotion at the milk company's office when no one there seems to know anything about a contest after the boys show up to claim their prize pulling a wagon loaded with a thousand bottle caps.
Wally and Beaver secretly order a Florida alligator from a comic book ad, planning to keep the creature in their bathtub. But when a tiny, baby alligator shows up in a shoebox instead of the full grown, 8-footer shown in the ad, the boys enlist the help of crusty alligator expert, Captain Jack, to raise their new pet.
June sends Beaver with a welcome-to-the-neighborhood bouquet to new next-door neighbor Mrs. Donaldson; but when the little boy is rewarded with a kiss on his cheek, rascally Eddie Haskell warns that a jealous Mr. Donaldson will soon show up at Beaver's door.
June makes Wally and Beaver sign a friendship pact to stop them from fighting and do more things together. But when each boy is offered a Saturday activity that doesn't include the other, they find the pact is not so easy to keep.
Beaver is left out when Ward and the other neighborhood dads offer to pay Wally and his friends for doing outdoor chores to help them buy uniforms. But, after Beaver finds out that the main water line will be shut off on a very hot day, he loads up his wagon with full water buckets and makes his own money ... at five cents a cup!
Beaver's crush on his teacher Miss Canfield and teasing by the other kids leads him to put a spring snake in her desk drawer. When his conscience starts acting up, he does his best to make sure the snake stays in the desk.
A rainy day indoors prompts Wally and his friends to build a clubhouse across the street. When Beaver can only join if he comes up with $3, he decides to hit the streets with a newfound entrepreneurial spirit.
Beaver suffers the consequences when June's beloved Aunt Martha comes to stay at the Cleavers and sends him to school dressed in her idea of what a young boy should wear to school...an old-fashioned suit with short pants and cap.
Wally and Beaver send for a supply of "Flower of the Orient" perfume to sell door-to-door, planning make enough money to buy a movie projector. But selling the perfume turns out to be harder than they think, especially when everyone agrees that it smells like an old catcher's mitt!
Eddie Haskell thinks it's funny when Wally and Beaver are grounded after he tricks them into going to the movie "Voodoo Curse" even though they promised June that they wouldn't ... until Beaver gets even by using a little "voodoo magic" on Eddie!
After having to listen to colleague "Corny" Cornelius brag about his children's academic excellence, Ward is thrilled to return the favor when principal Mrs. Rayburn calls to say that Beaver's score on an intelligence test is the highest in the school; but one of Beaver's classmates has a secret and Ward may have to eat his words.
Wally and Beaver get more excitement than they expect when give up their Saturday visit with Gus the fireman to babysit mischievous little "Puddin'" while her parents go with Ward and June to a wedding.
A package delivered to the Cleaver house from a high-end sports store seems to confirm Ward's suspicions that Wally and Beaver skipped school to buy expensive baseball mitts with piggy bank money they promised to deposit into their school bank account.
Busy Ward thinks his boys spend all their time over at the Dennisons' because they can play basketball there with their friends. But when Wally and Beaver still prefer the Dennison driveway, even after Ward puts up his own backboard, it takes a frank conversation with neighbor Chuck Dennison to reveal the secret that will bring the Cleaver boys back home.
Beaver gets a ticket and winds up in front of a tough traffic court judge after he and pal Larry are pulled over while taking a quick spin down the street without a license in a home-built race car powered by a lawnmower engine.
To impress the older boys, Beaver makes up a story about a real, live Indian fight that occurred across the street from the Cleaver house a hundred years ago and bets Eddie Haskell a dollar fifty that it really happened. But Beaver knows he's in trouble when Eddie and the boys show up with shovels to prove him wrong ... until they find what they think are valuable gems.
Concerned that Wally and Beaver are spending too much time at the movies on the week-ends, Ward plans a camping trip and the excited boys tell all their friends. But when Eddie Haskell's dire prediction that Ward never really intended to go camping seems to come true after unexpected office work forces the busy dad to cancel the trip, the disappointed Cleaver boys pitch a tent and spend a rainy night in their back yard to avoid giving Eddie the satisfaction of thinking he was right.
Cut during the first day of tryouts, Beaver tells his parents that he made it into the school band and carries his clarinet to school for weeks, thinking that he has plenty of time to tell them the truth; but time runs out when June finds a concert announcement in Beaver's pocket and the whole family plans to go.
Memories of companionship and comfort prevent Beaver from letting go of his well-worn teddy bear, Billy, and prompt the little boy to rescue his furry friend from the garbage truck even though Ward and Wally tease that he's "too old" to play with dolls.
Wally hedges after making a deal with his dad to paint the trashcans for fifty cents each, convinced by Eddie Haskell to hold out for more money. But when Beaver takes the job at the original price, causing hard feelings between the brothers, Ward looks for a compromise to satisfy everyone and finds, in the end, that boys will be boys and moms are full of surprises.
Initially impressed by Johnny Franklin's military academy uniform and good manners when Wally's former schoolmate comes to visit, June becomes alarmed when, as a result, Wally wants to attend the academy instead of Mayfield High with the rest of his friends.
In spite of Ward's misgivings, all goes well when Wally and Beaver volunteer to feed the neighbor's prize-winning cat, Puff Puff, until Wally breaks a promise, Beaver leaves a gate open and Eddie Haskell's dog chases Puff Puff up a tree.