Lampposts: The movie is set in New York yet shows side street lighting usually found in San Francisco. By 1967, half of New York had replaced street lighting with new aluminum poles, and those that had not been replaced would have seen the more common 'bishops crook' masts or 'long arm' poles.
Whilst in New York, Coogan is asked several times if he's from Texas, due to his cowboy boots and hat. Invariably Coogan responds that he's from Arizona. However, in the film's opening scenes, the badge on his deputy's uniform indicates that he works for the Piute County Sheriff. Piute County is in Utah.
The character played by James Edwards in this movie (the undercover detective on the stairs in Mrs. Ringerman's apartment) is called "Sgt. Wallace" during the movie. However, in the closing credits, he is credited as playing "Sgt. Jackson".
During the motorcycle chase, when Coogan follows Ringerman's motorcycle up two short flights of stone steps in the park, the stunt rider for Clint Eastwood clearly badly clips the stone wall with the right handlebar and loses control as he tries to make the right turn off the top flight. The film cuts to another shot before what would have been the inevitable crash.