According to Robert Osborne on TCM, this was a film that Jack Lemmon didn't really want to do, but by doing it he fulfilled a contract with Columbia. And, like the previous year's Under the Yum Yum Tree (1963), it stupefied Lemmon that they were both very successful films.
The name of the advertising firm for which Sam Bissel works, Burke & Hare, is a reference to William Burke and William Hare, two Irish laborers living in 18th century Edinburgh, Scotland who became notorious as history's most famous "body snatchers" who, until they were discovered by the British authorities, killed at least 16 travelers and then sold their corpses to medical schools for dissection.
One of or maybe the first demonstration of Velcro in a movie. Sam's wife has Velcro on her apron she's wearing in the kitchen that holds the oven mitts to it. The producers of the film make sure you hear the distinctive ripping sound of the Velcro as she peels off the oven mitts.
The interior of the Smiley Hotel, where Sam checks-in to access a billboard he needs to vandalize, is the famous Bradbury Building in downtown Los Angeles.
This was the final film appearance for Bess Flowers, one of Hollywood's most prolific extras/bit players, ending a career of approximately 41 years. As was typical, she was uncredited.