When Charlie wakes up John by bouncing on his bed and John pulls a gun on him, you hear the sound of a revolver being cocked. The gun appears to be a glock which has a completely different sound when being cocked and generally requires two hands, where only one was used when pulling the gun out.
Chasing the arsonist at Fulton Street, John tries to cross the tracks but is trapped momentarily between trains passing in both directions. At the same time Grace and Charlie are running along a nearby part of the platform, but the trains are not there; in fact, our viewpoint is from the opposite trackway below platform level.
We don't see all of the "Lexington Av & Queens" sign, but the part we see is for the E train. As the man is being pushed, we can glimpse a sign on another platform for F trains only, implying that the E and F have separate tracks at this station. Yet the train is an F. Later, when John and Charlie return to the station, the same platform is marked for both E and F trains.
The fight with the arsonist occurs in the tunnel near 5th Avenue station on the N line; the only other trains on this route are R trains. The train that ends the fight appears first as an S train to Times Square (which belongs 17 blocks away, on 42nd Street), then in the next shot it is an N train to Ditmars Blvd (which is right).
John rides his motorcycle into Times Square station, onto the platform, and then onto the track to ride in front of an advancing train. The signs on the escalator he uses show him heading for the 7 train's platform, but signs for the S train can be glimpsed on the platform, while the train is a 3 train!
When we see John about to twist the motorcycle through the pillars before jumping onto the track, there are only 2 more pillars to the end of the station. After the camera angle changes, he is much farther from the end wall and passes at least 15 more pillars within the station.
When Charlie is going down to steal the money train, we see him going down at the 110th street station, on the B and C lines. Moments later, just before Charlies lies down on the tracks, on a pillar behind him, it says 116th street.
Patterson has Grace, John, and Charlie in his office after the fight on the money train. After dismissing Grace, he locks the door to his office. Patterson's assistant enters the room to inform him of the confession.
Many instances where a line is shown with the wrong number of tracks, or station platforms are on the wrong side. For example, Wall Street (Lexington Avenue line) has outside platforms, not a center platform; Bowling Green station has no express track that would allow one southbound train to run through while another is at the platform.
The real money trains (officially known as "Revenue Collection Trains" of which there are several dozen cars in service, not two) are usually older, grungy, decrepit retired passenger cars with bars on the windows. They are painted yellow with black warning stripes in the front. They are staffed by NYC Transit Authority, a majority of which appear to be middle aged, overweight, and female, oddly enough, and armed with nothing more than .38 revolvers. They are nothing like the automatic weapon-wielding SWAT team cops depicted in the movie.
In a collision between a train car and columns, the columns would tear the train car apart. This has occurred numerous times in the past decade, most infamously in the Union Square wreck in '91, in which columns installed nearly 90 years earlier tore in half a runaway 6 year old train car.
The ticket booth windows in the New York subways are bullet-proof, so John would not be able to shoot out the window in order to save the clerk. Likewise Grace would not be able to shoot at "Torch" from inside the booth
It is impossible to "bleed the brakes" or otherwise dump out compressed air on any NYC subway car and force a runaway condition. When air pressure is lost on a subway car, it actually engages the brakes. This is a common fail-safe in rapid transit and railroad systems.
In the next shot from on board the money train after we hear it has passed 59th Street, it is running on the left. (Specifically on the second track from the left: the express track going the wrong way.)
The dispatcher doesn't think of clearing the track in front of the money train until it has run 6 miles from 110th Street to Grand Street, and it isn't making any stops for all that time, but it doesn't catch up with another train until after crossing to Brooklyn. (It does change from the local to the express track for some reason.)
The dispatcher, watching his monitor as the money train collides with a regular B train for the first time, immediately says "Oh my God." The monitor would not show information precise enough to identify that the trains had actually collided.
A crash that sends a railway car rolling along several tracks does not short out the power supply. Normal lighting is visible in the B train, and its route signs are lit, when people are getting off it.
A radio message dispatches emergency services to "Fort Hamilton" station, but there are three different Fort Hamilton Parkway stations on different lines (F, N, and B and M), so they would not know where to go.
John was not present while Charlie was getting beat up in the bar, thus making it seem like a goof when he says "Who you callin' nigger?" to Mr. Brown. However, the bartender later showed up at John's apartment to tell him about the trouble that Charlie was in, and it's possible that he told John what Brown said (assuming Charlie told the bartender, which, again, is possible).
At the time of the theft/hijacking, all the guards go to the token booth and none of them stays near the train to guard the money already on board, even though the train door is wide open to the platform. If one guard had stayed, Charlie would not have been able to break in unnoticed through the train floor.
Charlie climbs down onto to track level and lies on the track in front of the money train, all in plain view of its driver, as if he knows what's going to happen next -- the driver just stops the train right on top of him and says nothing about it to anyone.
Although nobody is changing the power settings on either train (the B train's driver is maintaining full speed and nobody is at the controls of the money train), for no reason the money train surges forward to collide forcefully with the B train six separate times, artificially creating the need for a device to stop the repeated collisions. Also, they occur at varying time intervals, artificially allowing time for the solution to be carried out.
When chasing the arsonist, Charlie fires a shot which frightens a horse in the street, causing it to run away. However, the shot does not frighten any of the other horses which can be seen in the street.
When the guy known as the torch first strikes, he confronts Grace in the subway who fights him before he gets away. Later Grace works undercover in the booth for the police to catch him. Why would they send in Grace to do this, the second time he strikes he remembers her from the earlier scene and would have known she was a cop.
At the end of John's confrontation with Mr. Brown in the strip joint dressing room, John delivers a roundhouse kick that sends Brown flying through the etched glass door. However, you can clearly see the stuntman playing Brown jump backwards through the glass a split second before the kick appears to connect.
NYC subway trains are electric, and get their power from a 'third rail'. This is an extra rail with a safety cover on the outside of the running rails - a 'pickup shoe' extends from each car and rides along the top of the third rail to supply power to the train. This third rail is notably absent in all shots where the rails are visible, because the real NYC transit cars used on the set were converted to run on propane.