When Shirley Temple is interviewing Cary Grant after his lecture at her high school, he refers to her as "Miss Kilgallen" instead of her character's name of Miss Turner. This is a reference to Dorthy Kilgallen, a popular American journalist of the time.
When filming began, Shirley Temple was 18 years old and had been married for 10 months. Cary Grant was 42 years old.
A couple of in-joke references to Shirley Temple appear in the film. When Cary Grant is sitting with Shirley in the soda shop, the waitress serves him a "Shirley Temple" drink. Later, when Shirley is in her room, packing her suitcase, she takes a Shirley Temple doll off the mantle over her fireplace.
The "man with the power" routine was the inspiration for the song "Magic Dance" in the movie Labyrinth (1986).