Continuity mistake: In the opening sequence, Felix (Jack Lemmon) goes into the Metropole Cafe. One of the people he passes as he enters is a young woman with a thin face and very distinctive nose and eyes. He goes in, has a drink, hurts his neck, and leaves. As he is leaving, the camera pans the band and go-go dancers. One of the dancers is the young woman who had just left as he was entering.
Plot hole: During the first poker game of the film, Vinny (John Fiedler) picks up one of his poker hands and straightens the cards in such a way that everyone else at the table can see them. Since the other guys gripe about how much Vinny is winning, neither Fiedler nor director Gene Saks must've known that his cards were visible.