When Stu's wife is with the police trying to talk Stu out of the phone both she tries to say "Do what they tell you to do, Stu!". Instead what she actually said was "Stu what they tell you do!". (When putting on the subtitles for the movie it confirms she was supposed to say "Do what they tell you to do, Stu!".)
During the first couple of scenes inside the booth, the sticker on the receiver is worn out and barely readable. After the first close-up the worn out section of the sticker is replaced with a new part, boasting clearly the name of the phone company.
As Stu falls to the ground the initial shot shows the phone receiver swinging on the end of the cord. The reverse angle shot immediately after shows Stu still falling, but the receiver and cord are now hanging dead still.
Although the film is set in New York, it was filmed in LA. When we see news reporters arriving, there is a shot of a female reporter in the bottom left of the screen. An LA public transport bus can be seen passing by in the background.
The caller's intent to frame Stu for the murder of the pimp is flawed in several ways. Firstly, Stu would have had no gunshot residue on his hand. Second, hollow-point bullets do not fragment on impact, but flatten out to achieve a larger wound, so there would've been a bullet left behind. Third, when investigating deaths by gunshots, the investigator fires comparison bullets to help match the bullet found in the victim or the wound caused by the bullet. Fourth, the entrance wound would show that the pimp was shot from behind, but when he was struggling with Stu they were face to face, meaning Stu couldn't have possibly shot him in the back from that position.
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 story. 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.
When the caller/sniper gets a bit twitchy, threatening to shoot Stu's wife and the police officers, we hear him cocking the rifle five separate times. At no point do we hear him un-cocking the rifle between those moments, but he would have to physically cock and load the rifle every time he needs to fire a round. But since there are two rifles in play (one left with the dead pizza guy, and one the Caller carries in the final scene), the Caller could easily have had an empty rifle that he cocked, seeing how he uses the sound to intimidate Stu.
At the end of the movie as Stu (Colin Farrell) lies in the ambulance after being shot, he is given medication for the pain which makes him very disoriented just in time for The Caller (Kiefer Sutherland) to show up and taunt him. The person who administered the medication just hops out of the ambulance. Any time an injured person would be given such a strong medicine, they would be monitored to ensure that they have no negative reaction.
No red dot laser designed for targeting would be visible in daylight at the distance shown, especially on a dark surface such as the black suit jacket worn by Stu. The red dot seen in the film is a crude optical effect.
When the camera pans on Stu coming around a corner to the phone booth, extras (especially one with a box) can be seen standing very still and not moving. Only when Stu comes around the corner do they start moving.
The goof item below may give away important plot points.
In the moment where Stu is shot with a rubber bullet, you hear a shot ring out, and you see Stu shake, then fall to the ground. Shortly after, when he is speaking with Captain Ed Ramey, you see the location on his chest where the bullet supposedly hits him, around the center of his chest, near the 3rd button from the top on his shirt. Despite this, at the exact moment when he is shot, you cannot observe any indication that anything has hit him in that area. There is no sign in the visible target area that anything has hit him at all. His shirt shows no sudden movement which would indicate the hit of the bullet. If a rubber bullet did truly hit him in that area, his shirt should at least crease at the area of contact, or possibly even rip.