When John is playing pool with Robbo, and running the table, the position of the balls on the table change between shots, and he appears to sink the same striped ball twice.
Although an exact year isn't given, internal evidence indicates the film is set in the early 1930s,and certainly during Prohibition. However, there are women serving on the jury at Robbo's trial, and women were not permitted to serve on juries in Illinois until1939.
When Will (Sammy Davis Jr.) is shooting up the casino, he fires more shots than either gun holds (12 from one, 11 from the other).
During "Mr. Booze," John (Dean Martin) repeatedly hits his tambourine out of rhythm with the rest of the chorus, yet there is no sound of his tambourine playing.
During Will's song and dance following the destruction of Gisborne's casino, Will kicks a tray of intact plates and cups. Most of the plates and cups are seen to be broken as they fly through the air before they hit the ground (when they should have broken), showing that they are already "broken" props.
At the funeral when Richard Bakalyan plays "Call to the Post" on a Bb trumpet in the key of Bb he fingers the valves. This would be played with only the first valve down for the entire time.
During "You Got to Have Style" number, the actors' marks are visible on the carpet.
When the cornerstone for the police station is being dedicated, and again when the pretzel factory cornerstone is being dedicated, mountains can be seen over the rooftops of the buildings in the background. There are no mountains in Chicago.