When Naomi and Arthur enjoy their "first date" in the middle of Grand Central Terminal, darkness is seen outside the windows as if its the middle of the night, even though they were in bright daylight moments earlier outside on 42nd Street.
When the semi-naked Arthur is talking to Naomi from the street, the onlookers behind Arthur (who are genuine passers-by, not extras) change from shot to shot and back again. There are two distinct groups of them, revealing that two separate takes were intercut to create the final scene.
In their first encounter, Arthur accidentally shoots Burt with a nail gun in his arm and shoulder. Then, when Burt is threatening Arthur with the saw, there is a bloodstain on Burt's shirt, but no hole.
Near the end of the movie, outside Naomi's apartment, Arthur states "My mum's dead." It was his Nanny, Hobson, that passed away, but she was more of a mother than Vivienne ever was, and Naomi would know that. (This is also parallel to the original film, in which Arthur tells a drunk "My father died" after the passing of Hobson. Arthur's actual father was still alive and well in the film.)