Plot hole: When they get Sam the driver off the bus and onto the trailer, it's stressed how important it is to get him to hospital, but in all subsequent scenes, the trailer never leaves the side of the bus and no-one takes Sam off.
Continuity mistake: Travis shoots Harry in the leg, and Harry is slumped against the wall next to the doorway. When Payne sets off the bomb, Harry is now no longer near the door, and is halfway down the corridor. Not enough time had passed between shots for this to have occurred. (00:22:20)
Continuity mistake: When the subway carriage bursts out into the street, Annie's handcuffs slide off the broken pole and in slow motion you can see the pole is shorter than all others. Besides, all the other poles in the carriage are intact. (01:49:15)
Continuity mistake: When Keanu and Jeff are on their way to the building at the start of the film, their car flies over a hill and lands back on the road. The right hand front wheel takes a really nasty knock as it lands and looks ready to come off, and yet in the next shot they arrive safely with no apparent difficulty driving the car. (00:06:00)
Continuity mistake: After the bus driver looks at the note "Bomb on Bus" he starts decreasing speed. So Keanu puts the Jaguar beside the bus and tells the bus driver to open the door for him to tell the driver to go at a speed of 50 miles per hour. Just before this you can see a camera shot in which the door is already open. This mistake is easily seen if you watch it in slow motion.
Continuity mistake: When Howard Payne is in the elevator, he hears Jack and Harry doing something from above, and he reaches for his bomb trigger. In slow motion when he's picking it up, it has two buttons on it, yet when Howard pushes one of the buttons, the device now has three. (00:13:00)
Plot hole: Payne's finger prints would've been all over the elevator, on his shotgun, and near the area where he killed the security guard as he was never shown wearing gloves. Since he was a former police officer, I would assume his prints would've been on file with the FBI and in a multitude of databases. You would think they would've been able to identify him much earlier in the movie than they did by running the prints through all databases of finger prints.
Plot hole: The police thought they could catch the bomber at the ransom drop because he did not know that the bus had exploded. However, the exploding bus would have created a huge plume of smoke that would have been reported by the media. (01:30:00)
Stupidity: Howard has the opportunity to shoot Jack at the end, but doesn't for no discernable reason; he's already committed multiple felonies, and shooting Jack would help cover his tracks all the better. In fact, he could even have just taken the cash onto the subway and left Annie behind while staying in full disguise as a cop.
Other mistake: When the safety cable goes taut and stops the falling elevator, a woman standing in the corner is shown to fall through a hole in the floor. However, the hole in the floor was plainly visible in the bottom of the elevator as it was falling. As the hole was more than wide enough for the woman's legs to fall through, she couldn't have been standing in that corner as it was falling.
Plot hole: It is never definitively stated if the bomb is tied directly to the axle, triggered by the speedometer instrumentation or throttle. Regardless, as long as the wheels keep spinning above 50mph the bomb will not explode by design. This means that if you lifted the wheels of the bus off the ground or you bottom out, you could keep accelerating without any speed at all. This could be accomplished in any number of ways. One example would be driving on grass and keeping the tires spinning.