Factual error: When Renee Zellwegger arrives in New York, she exits her cab in front of the United Nations. The Canadian flag is visible. The movie is set in 1962, and the form of Canadian Flag in the shot was not adopted until 1965.
Factual error: David Hyde Pierce mentions the Cuban Missile Crisis, which took place in October 1962. The time of year in the movie isn't entirely clear, but given the weather conditions it's almost certainly spring or summer, or several months before the Cuban Missile Crisis.
Continuity mistake: At the start of the movie, when Barbara crosses the road from Grand Central Station to catch the taxi, there is a blue car parked in front of it. Then when the shot is shown from the rear of the taxi, the blue car is gone. When the shot moves back to the side view, the blue car is back there again. In addition when the shot is taken from the side of the taxi, there is no green fence visible, however, when the shot is from the rear of the taxi, there is a shoulder-high green tubular fence on the footpath.
Revealing mistake: Toward the end of the film when Catch has been left on his own by Barbara, and it begins raining heavily, he doesn't look like he is getting very wet. As the shot pans out, you can see on the street, that the rain is falling everywhere except for a perfect square around Catch, due to an off-shot prop.
Factual error: At the end of the movie mention is made that Catcher gave Barbara his publisher's Celestron telescope, shown earlier in a scene where the two are looking at the moon. This was probably product placement, but the C10 design shown in the movie was not offered by Celestron until 1964 (the film is set in 1962) and it sold for a price of around $2000, not $6000 as stated in the movie.
Visible crew/equipment: In a scene where Peter is coming over to Catcher's apartment, the microphone is visible on the top of the shot. It is quickly removed once Catcher looks behind the camera.
Continuity mistake: In the scene where Ewan MacGregor is telling his workmate that he will make Renée Zellweger fall for him he is holding a drink in one hand and an olive on a stick in the other. As he speaks he is gesticulating with the olive, then he eats the olive, then it re-appears on the stick.
Continuity mistake: When Catcher and Barbara walk out of the laundry service and start talking Catcher's teeth are yellow and not very clean but in the next shot they are beautifully white. This happens again and again.
Continuity mistake: In the scene where Barbara and Vikki enter the Mahogany Room for the first time, when Barbara takes off her coat, she leaves her purse with the attendant and takes off her gloves as she walks towards the table. In the next shot, she no longer has the gloves but now she has her purse.
Factual error: The last scene has the lit-up Verrazano Bridge in the background as Renee Zellweger and Ewan McGregor swoop over Manhattan. The movie is set in 1962, and the bridge wasn't built until 1964.