Continuity mistake: Towards the end, the line in the play is "The princess is here" an a carpet pulls down the stairs and across the stage. The carpet is a straight line down the stairs. They cut away and when they go back, the carpet is neatly folded into the stairs so the princess can walk down them.
Continuity mistake: During the rehearsal, Bixby throws a temper tantrum and kicks the piano. It slides straight toward the curtain, but in the next shot, it's spinning around. In the shot after that, it disappears altogether. (00:26:10)