Continuity mistake: When they give Garber the pistol to take, it has actually changed when he pulls it out of the bag, it's an entirely different pistol.
Other mistake: While a sniper is awaiting permission to shoot, a rat crawls up his leg and bites him, resulting in an accidental discharge. A trained shooter, much less SWAT sniper, knows that you never place your finger on the trigger until you are prepared to shoot. Otherwise, you could have an accidental discharge.
Revealing mistake: After Garber shoots Ryder, he is told by the approaching policemen to "drop your weapon". At which point the camera pans to a shot behind Garber where he is holding the gun in his right hand and proceeds to drop it. Watch the bottom of the screen and you will see Garber catch the falling gun with his left hand.
Factual error: When Pelham 123 gets split in two (as in it's uncoupled from the rest of its train), they do so from a control panel from the inside of the car above the seats. Subway cars, like all rail cars, can only be split manually through a lever near the coupler, not through a control panel. In addition, subway cars have ropes between cars, which must be taken down before cars are split. Otherwise they will still stay connected.
Other mistake: When Regina first speaks into the mic, she doesn't press the button so they shouldn't be able to hear her. (00:11:50)
Other mistake: When they give Garber the pistol to take, the cop shows him how to operate the safety. He releases the safety and says it is safe, then puts it on safe and says it is ready to shoot.
Continuity mistake: Towards the end of the movie when the single train car is rushing down the Coney Island bound F line, you see different camera shots of the train above ground. One of the shots shows the train speeding past Shea Stadium, which is actually located in Queens on the 7 line.
Plot hole: During the scene where Ramus is shutting down the power in the tunnel, he shoots off a padlock with a gun with one shot. Aside from being quite dangerous at close range, both Mythbusters and Masterlock have proven this cannot be done with an ordinary gun and ammo, and certainly would be unlikely with one try. I know this used to be run-of-the-mill stuff in movies, but it does not fit modern research that has been done concerning the strength of padlocks vs using guns to open them.
Factual error: The 6 subway runs from Pelham Bay Park in the Bronx to the Brooklyn Bridge stop in lower Manhattan. How the subway switches to the F line to Coney Island which is not connected to the 6 line is not explained. It is not possible as the tracks do not cross.
Continuity mistake: The Brietling John Travolta is wearing is different from scene to scene when he is on board the train. One watch has 3 dials; the other none.
Other mistake: In the scene where Garber is in the helicopter, the far away shot shows it as being almost sunset, when it is actually closer to 3:30. The sun is low on the horizon.
Factual error: When the bad guys go though the hidden exit, they're identified at being around 33rd street. They take an elevator up to the Waldorf Astoria kitchen. This is impossible as the Waldorf is on 50th Street.
Continuity mistake: The money car gets hit by an ambulance on its way to the drop and rolls over. The light bar on top breaks off. It reappears when the car falls off the bridge. (00:59:10)
Other mistake: Following the scene where Phil Ramos is shot in the head by the sniper, you will notice him still breathing behind Ryder showing him in the background when Ryder gets on the radio.
Revealing mistake: The police car that transports the money is not what is used in actual police work. The all dark blue and white accents you see in the film is a color-scheme used in traffic cars and school safety cars. The real police cars are white with dark blue accents.
Continuity mistake: When Ryder first walks into view over the Internet feed from the laptop, he is wearing a greyish T-shirt (most likely short-sleeved as well). In the next shot, still on the feed, he's wearing a black leather jacket, the same one we see him wear since the beginning. (01:01:20)
Continuity mistake: When Ryder gets Garber to sit down in the cab, there is a bullet hole in front of Garber, when the train moves, the bullet hole is gone. (01:12:00)
Suggested correction: The bullet hole in the window was not directly in front of Garber. Ramos was shot through the window when he was sitting on the left side, the driver's side is on the right. When Garber sits down in the driver's seat he's at an angle when the bullet hole comes into focus. All other shots of Garber without the bullet hole are showing him straight on where the bullet hole cannot be seen.
Revealing mistake: Just as the train with the mayor starts moving, the film crew is reflected in the windows. (00:19:00)
Continuity mistake: When the train rushes through the first station, we see the slipstream take a load of paperwork and pass the station, camera cuts and they are just going past the station again. (01:17:45)
Continuity mistake: When Garber hands the hostage negotiator the page with his notes, the way Ryder is written changes. (00:24:40)