Revealing mistake: When Walther Matthau is making sandwiches for his poker pals (during the movie's first poker game), Matthau drops a slice of bread on the kitchen floor. If you look at his hand, you'll see that he flicks his thumb to make the slice of bread fall.
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.
Other mistake: In the opening credits, the copyright year is shown as MCMXLVII (Roman numerals for 1947), when it should be MCMLXVII (1967).
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.
Continuity mistake: At the baseball game Oscar is sitting and eating a hot dog, when the other guy answers the phone he is sitting there typing with no hot dog. When they cut back to Oscar he is sitting with the hot dog again.