Other mistake: In the opening credits, the copyright year is shown as MCMXLVII (Roman numerals for 1947), when it should be MCMLXVII (1967).
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.
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.
Character mistake: After Felix arrives at Oscar's apartment, he is looking out the window and comments on the view. He then asks, "What is it, twelve floors?" He had just come up in a self-service elevator, so he would have known what floor he was on.
Factual error: During the opening credits, Jack Lemmon walks past two "sailors" in dress whites. If they were actual sailors, they would have rate insignia on the left sleeve, service ribbons on the left breast, and a rocker patch on the right shoulder seam.
Character mistake: Shortly after Felix arrives at Oscar's apartment, he goes to a window and asks if it's 12 floors. Oscar rushes over, slams the window shut, and says it's only 11 floors. Since Felix had to push the button in the self-service elevator to get to the correct floor, and since he had been to the apartment many times before to play poker, he would have to know that it was 12 floors.
Continuity mistake: When Oscar and his pals are in police car number 578 out looking for Felix, suddenly they are in car 956; car 578 pulls up next to them (with real cops in it) to see what the problem is. (01:38:24)
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.