Factual error: The Caller tells Stu that Channels 2 and 5 were coming to see him. This would be correct, since Channel 2 is the CBS affiliate for New York City, and Channel 5 is the FOX affiliate, but the news vans that show up indicate that channels 5 and 8 are covering the stories. The nearest broadcast Channel 8 is in Connecticut. (The only channel 8 in the New York City area is used by a cable station for a premium channel or local programming.)
Continuity mistake: Several times during the movie the police cars forming the perimeter around Stu appear to be closer than they were before. When Captain Ramey first approaches Stu, he has to walk a distance of about half a block. Later in the film he seems to be walking only a few feet.
Factual error: Several times, throughout the movie, Stu or another character using a cell phone is hung-up on. When they are hung-up on, instead of the cell phone dropping, they hear a short dial tone. Actually, when a call is dropped, the cell phone side simply disconnects. You never get a dial tone.
Revealing mistake: When Stu is tempting the sniper to see if he will really shoot, the sniper shoots the phone booth, shattering the window, and supposedly hitting or grazing Stu's right ear. When Stu lifts his head, you can see his bloody ear. A few shots later, Stu's head is turned so you can clearly see his fresh wound. If you look closely, you can see Stu's real ear folded back beneath the fake latex one. This happens several more times in the next few minutes of the movie.
Plot hole: Why wouldn't the police evacuate the area around the booth where an armed (they think) homicidal maniac is making a phone call? All those people would be well within gun range and the city would have been held liable had any of them been shot. Step one is usually to secure the scene for the safety of the public.
Factual error: At the end of the film, the police just let anyone walk around the crime scene: in addition to the caller you also see various tourists gathered around the phone booth. The police would never ever do this: as Leon the pimp was murdered right by the phone booth it is a crime scene and as such must be cordoned off for the forensics team to arrive, instead of letting people contaminate the crime scene. Even though the police "know" the pizza guy did it, they still need to look for forensic evidence.
Factual error: The recreation of West 53rd St. is full of mistakes. The street, for example, is mysteriously as wide as an Avenue. The curbs are much higher than they should be, and the buildings are set back much farther from the street than they should be. Studio 54 and the Ed Sullivan Theater should be on the north side of the street, and the back of Roseland should be on the south. There is a subway entrance in the scene that's a block west of where it should be. This is not surprising as the film was shot in Los Angeles, not New York City.