When Marcia Warren (Jeanette MacDonald), Homer, and Cleona go to the movie theater, there's a large portrait photo of Nelson Eddy on the back wall. Nelson Eddy co-starred with Jeanette McDonald in eight MGM musicals from 1935 to 1942.
This was Jeanette MacDonald's last film on her original MGM contract. She made just three more feature films, one for Universal (Follow the Boys (1944)) and two more for MGM (Three Daring Daughters (1948) and The Sun Comes Up (1949)).
At one point in the film, when "Homer" asks "Marcia" if she has ever been to San Francisco, she replies "Once with Gable and Tracy and the joint fell apart," referring of course, to the very popular 1936 M-G-M film San Francisco in which Jeanette MacDonald co-starred with Clark Gable and Spencer Tracy.
The film sequence which Homer is watching ("for the eighth time") in the first reel is one of Jeanette MacDonald's arias from Maytime (1937).
Although Nelson Eddy's photo is hanging in the lobby, the film playing in the movie theater must have been the 1940 picture The Philadelphia Story (also MGM), because the music from the opening credits of that film can clearly be heard behind the characters' dialogue.