In the opening scene, Eve and Kaye are discussing an unnamed movie they saw in the theater the previous night. They describe the movie as starring Julie Andrews and Richard Crenna. Though they never mention the title, the actual movie is 'Star!', which premiered in the US on October 22, 1968.
Near the end of act I, Eve says "Baby, it's cold up here" in reference to the song "Baby It's Cold Outside".