Other mistake: When Captain Spaulding first arrives near the beginning at the movie, he takes his hat off twice.
Continuity mistake: In the very first scene, after the lead flunkie finishes his song, he turns around to speak to Margaret Dumont. When he turns back, look closely at his waistcoat - it's completely different.
Continuity mistake: Arabella places her left hand on her cheek with the index finger extended and jokingly asks her mother, "What do you suggest, a suicide?" In the long shot, her hands are pressed together and her fingertips are touching her chin.