Hal falls madly for Bunny, a swinging chick who comes on to him during a Sadie Hawkins dance. "You look just like Robert Redford!" exclaims Bunny. Hal is smitten by Bunny's feminine wiles.
After Bunny imparts that she is fifteen years old, thirteen year old Hal tries to impress her by claiming to be sixteen. Complications ensue the next day, when the assertive Bunny calls Hal and asks him to pick her up for the movies. Flustered Hal blurts out that he will be right over, in spite of the fact that he is too young to drive.
Nanny decides to bail out Hal, and she gives him a ride to pick up Bunny. Bunny is confused, and perhaps suspicious as to why Hal isn't driving, but Nanny explains she is driving because that "she loves to drive - even in Los Angeles."
While at the movies, Francine, Hal's thirteen year old next door neighbor sits down in front of Bunny and Hal. Francine, who has a crush on Hal, expresses surprise to see Hal with a high school girl. Bunny reacts icily to Francine
Prudence tries to get her seeds to grow faster while the Professor upsets his new girl friend when he doesn't try to save a dying tree.
The Professor tries to get out of playing football with his friends.
Nanny's Uncle Horace (Ray Bolger) visits from the South Seas to perform a rain dance in order to cure a drought.
Nanny's pychic aunt (Elsa Lanchester) predicts Nanny will be menaced by a man with a mustache.
Nanny's fiance arrives to claim her hand in marriage. The marriage had been arranged by their families on the day Nanny was born. They ask the Professor if he will give the bride away. The children and the Professor are upset by the thought of losing Nanny. She tries on her great-great-grandmother's wedding dress. Along with the dress is a note written by her mother which makes it clear the decesion to marry "Chumley" must be her's and her's alone. Nanny decides she's not rady to leave the Everett household.
Butch, thinking he is a jinx, is given a good luck charm from Nanny's Aunt Henrietta (Elsa Lanchester)
Nanny is accused of being a witch. (30 years later actress Juliet Mills will portray on witch on the daytime drama Passions)
The Professors RICH brother (Robert Sterling) donates two million dollars to his brothers college.
Aunt Henrietta (Elsa Lanchester) believes there is a ghost in the house because the furniture is disarranged every night.
Hal enters a golf tournement using strange clubs given to him by Nanny
Nanny and Hal help the Professor keep a basketball player from failing math.
Hal tries to visit his uncle, but doesn't quite make it.
Nanny trades in her old car "Arabella" for a new one
Prudence, being ignored by her brothers, becomes attached to Nanny's old doll.