A couple of times we see the characters sitting in a bar, while a snowstorm is obviously occurring outside, but when they walk outside, there isn't any snow on the ground at all.
When arriving back at her apartment after the dinner with Jack, and they play the phone message, Lee and Jack are wearing different clothes.
The real Jack Hock was American, not British.
The word " backstory " is used, despite not being widely used at the time this story takes place.
Rolled thermal fax paper would have been used for the fax machines, not plain paper as represented in the time period of the movie. Plain paper fax machines did not come into use until much later.
When Lee is seen walking toward the 86th Street subway station, she passes the Citibank branch at 86th and Broadway, with an advertisement for Citi Priority Banking in the window. Citi Priority did not exist until 2016.
When Lee is seen walking toward the 86th Street subway station, a sidewalk fruit stand is seen in the background. Fruit vendors were not common in New York until 2008, when the city's Green Carts program was implemented.
Twenty-first century automobiles vaguely drive around in some shots.
Lee leaves her sickly cat with her blatantly irresponsible friend Jack and stays overnight in New Haven to steal a letter from the Yale library. New Haven is less than two hours from New York. She could have fed the cat, gave him his pills, arrived in New Haven when the library opened and been back in time to feed him again, and go back the next day if necessary without spending on a hotel and food.