The musical number Kate rehearses for the amateur show, "Any Way The Wind Blows," had been written for Doris Day's previous film Pillow Talk (1959). The song title was, for a while, even the working title of that film.
Beginning her feature-film career portraying Katharine Hepburn's mother in Little Women (1933), Spring Byington closed her movie years playing Doris Day's mother in this film. She would go on to work in television, most notably as Aunt Daisy Cooper on Laramie (1959).
This was one of several projects in which Doris Day performs her signature song "Que Sera Sera" from The Man Who Knew Too Much (1956). Here she sings a verse from "Que Sera Sera" to David Mackay in an Italian restaurant.
In an early example of product placement, Quaker Oats is featured prominently in the film due to a cross promotion with the producers. In a national ad campaign, Quaker offered children under 12 free admission to the movie if accompanied by an adult. Each "specially marked" box of Quaker Oats contained an "MGM ticket" good for one child's admission when accompanied by someone over the age of 12 paying adult admission prices. The April 18, 1960 issue of Life magazine features a full page ad (page 18) on the promotion, and can be found on Google Books.
This same source material was later the basis of a sitcom with the same title that ran for two seasons on NBC in the mid-60s.