Continuity mistake: Brophy and Dr. Thorndyke are in the bathroom. The lid of the toilet is ajar, then is suddenly closed properly.
Continuity mistake: The tissue paper in Professor Lilloman's right hand instantly jumps to his left as he gets up out of the chair in Dr. Thorndyke's office.
Continuity mistake: In Dr. Thorndyke's office, Dr. Montague holds a pencil in both hands in the front view of him, but the view over his right shoulder shows him holding the pencil in his right hand.
Continuity mistake: After stabbing Thorndyke in the shower with the newspaper, Dennis drops it behind and to his left. The next shot and the newspaper is seen inside the shower tub, close to the drain as the ink runs off the paper into the drain.
Continuity mistake: The piano player speaks into a microphone in the close up, but disappears in the long shot of him.
Continuity mistake: Dennis, Thorndyke, and Brophy are shown in the close up getting up together outside the elevator, but the long shot shows Dennis already standing three to four feet behind Thorndyke and Brophy as those two stand up.
Deliberate mistake: After the hotel murder, Brophy makes a series of photographic enlargements to prove Dr. Thorndyke's innocence. However, instead of holding his magnifying glass directly in front of his face as he examines the photos, Brophy angles the magnifying glass far to his right so the movie audience can see the magnifying glass details, but he can't possibly see anything.
Answer: It was a song written by Mel Brooks for the film. It's called "If You Love Me Baby, Tell Me Loud."
Bishop73