(at around 24 mins) After Chapman signs his name as John Lennon, his co-worker notices it and starts to walk out after him. The next shot is a long shot from outside the building, showing the co-worker still standing behind the desk. Then in the next shot he is walking out the door again.
(at around 28 mins) Mark David Chapman used a cheap Charter Arms .38 Special snub-nosed revolver to murder John Lennon, not a Smith & Wesson as is described in the movie.
(at around 1h 14 mins) When Mark shoots John Lennon, he shoots eight times. Historically this is inaccurate, Mark David Chapman really shot only five bullets, with four making contact.
(at around 57 mins) When the prostitute that Mark hires takes the elevator up to his hotel room she exits the elevator on the 37th floor, but Mark David Chapman's room was on the 27th floor.
(at around 54 mins) When Mark imagines shooting the two gay men, the blood pack is visible when the man on the left gets hit.
(at around 30 mins) When Chapman is riding in a taxi at the start of his first trip to New York, he is driven through Times Square. A number of stores that weren't in Times Square in 1980 clearly can be seen, including Foot Locker, a Virgin Megastore and Planet Hollywood.
(at around 30 mins) When Mark Chapman is on his first taxi ride through Times Square, large Broadway posters of Wicked and Hairspray are clearly visible in the background. Both musicals only began their run within the last 9 years.
There are a number of street signs shown throughout the film that are green and white. In 1980 the street signs in New York City were yellow and black.
(at around 51 mins) When Chapman is walking through a subway station in New York City you can clearly see the turnstiles that use metro cards. In 1980 you still had to use tokens to enter the subway. Metro cards weren't in use until the late eighties.
(at around 34 mins) When Mark is coming out of the bathroom from taking a bath on his first New York trip, he goes toward the door, getting close to the camera. If you look in the mirror behind him (watch for when he bumps the door), you can see the camera guy holding the camera and backing up a bit when the actor comes toward him.
(at around 1h 45 mins) In the flashback of Mark Chapman riding through the city in the cab near the end of the film, the camera is clearly visible in the reflection of the rear windshield.
During his first taxi ride in New York, they are driving through Times Square and Chapman eventually is dropped off at the Waldorf-Astoria Hotel. During the ride, the driver says they're about to pass John Lennon's home, but the Dakota building is on Central Park West and 72 Street. Times Square is in the lower to mid 40s at 7th Avenue and Broadway and the Waldorf-Astoria is on Park Avenue in the upper 40s, so to get there all you have to do is go across town a few blocks. The taxi never would be anywhere near the Dakota.