On Vicki's bedroom wall is a print of the painting "Pinkie" by Thomas Lawrence. In 1949 Jeanne Crain (Jill Lynn) starred in the movie Pinky.
The use of the quote, "The butler did it," was at that time a recognized joke. It played off the spoiling of the ending of a play or movie by a big mouth in the audience. It did not refer to the plot of the film being shown in that theater.
When Jill Lynn (Jeanne Crain) seeks out Steve Christopher (Elliott Reid) in the all-night movie house, a film is playing on the screen but we only hear the voices. The dialogue is from the classic movie Laura, and the lines are from the police interrogation scene featuring Gene Tierney and Dana Andrews. However, when Christopher jokes about the movie he's seen 4 times, he is referring to something completely different (he mentions "The butler did it").