When Paula tells Elliot that somebody stole her purse, there is a NYC Police car in the background. Additionally, when Elliot confronts the muggers at the red light, there is another NYC Police car right before the intersection in the left corner.
The brass, square doorbell button mounted on the door to the apartment sounded with an electric buzzer sound when pushed. This doorbell is actually a mechanical, spring loaded model which sounds a "ding dong" as one pushes the button in and then releases button. The mechanism is on the opposite side of the door and can be seen in later scenes. One typically sees these on office doors, small apartments, mobile homes, etc.
When Elliot returns home drunk, prior to opening the window, he knocks over a white table, spilling everything and leaving the table bare. The next shot is of Elliot outside the window, reading a bad review (11 seconds before Paula starts to pull him back inside). The following shot from inside the apartment shows the table with all items returned properly (but not to the same positions). Although it's possible Paula reset the table, it's unlikely that she was able to reach all the items and return them to proper positions so quickly.
When Paula falls in the street, a box of spaghetti remains intact. But when Elliot goes back to help her, the box is open and spaghetti is strewn on the ground. Also, Paula is now beside a completely different parked vehicle.
When a drunken Elliot leans out of their apartments bay window to yell at the world his body drags the curtain with him. But in the next exterior shot there is no curtain visible, and in the next interior shot the curtain has disappeared from the window altogether.
When Quinn Cummings pulls the old style flip-top off the can of soda it breaks leaving a sharp piece sticking out of the opening of the can. Quinn sees it, but continues the scene with barely a flinch. Pretty amazing for a 10 year old.
Based on a previous reference, the movie takes place in the early spring (also note how trees have yet to bud out). Thus, the time period of the film is late March. During a morning conversation between the two lead characters, Mason notes that it's 5:55 a.m. However, the high level of light outside the window would have been impossible at that time of day in the early spring. The scene appears to have been shot in the middle of the day, not so early in the morning.