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 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.
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.
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.
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: 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.
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.
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)