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!