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.
Suggested correction: It is unlikely, but they could have transferred him a second time to another vehicle off-screen.
It could've happened during the scene where the older scared woman was trying to leave the bus, and the cops told her to "grab my hand." They KNOW the hostages leaving the bus risks the bomb going off, and they still tried to get that lady off. It's literally these cops' first day on the job.
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)
Suggested correction: Harry drops to floor by door 1 on the right-hand side of the corridor facing the parking lot. We then get a 2-3 second shot of Jack shrugging and shouting "Freeze" at Howard. Howard is then seen staring at Jack in disbelief at the thought of him shooting a hostage. We then see Howard (still in the initial 3 seconds) walk into the parking lot and Jack run towards the door. As Howard is going through the door the shot changes to Jack and in this shot you can see Harry shuffling down the corridor.
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)
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.
Suggested correction: Howard Payne's taunting dialogue in the subway station suggests that he wants Jack to live a long life, tormented by the fact Payne was able to beat him. He doesn't become intent on murdering Jack until the dye pack goes off, ruining the money. After that, he tries to shoot Jack but runs out of bullets, then decides to beat him to death with the detonator but fails.
Continuity mistake: When Jack and Harry are pulling people out of the elevator there are two men offering to help the stubborn lady out of the elevator. 2 seconds later there is only one man jumping to get out. (00:15:50)
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.
Suggested correction: IAFIS, the FBI fingerprint database, wasn't implemented until 1999. At the time this film was released, the LA police would have to individually run any prints found through the databases they wanted to search. Essentially, they would have to know beforehand that Howard Payne was a former Atlanta police officer or have made a wild guess.
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)
Suggested correction: The news reporters at the airport had been blocked by the Police from reporting. Reporters that weren't at the airport would see a cloud of smoke but wouldn't know what was causing it.
Yes, but the reporters would still report it, and the bomber would know what had caused it.
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.
Revealing mistake: When Payne opens the money bag to see a dye bomb explode, he is wearing a transparent protective face shield (partially visible). (01:42:35)
Suggested correction: This needs clarifying. The dye looks like it goes directly on his face in real life, and no protection is visible at all.
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.
Suggested correction: And that would accomplish precisely nothing. They know Payne is watching them and he explicitly stated no-one is allowed to get off the bus or he will detonate it, only making an exception for the injured driver. What good is finding a way to keep the wheels in motion if everyone is still stuck on the bus?
The mistake is suggesting that you basically find a way to stop the bus but keep the wheels spinning such as grounding it on a hill. Then while the bus is stationary, just (I'm assuming here) put a weight on the accelerator to keep the wheels spinning and then everyone just hop off and walk away. However, you're correct in that Howard is watching the live feed so would just blow the bomb when people got off.
I fully understood what the entry was suggesting, but Payne's demand that everyone stays on the bus under penalty of detonation voids it. Even if that wasn't the case, finding a way to somehow stop the bus but keeping the wheels spinning (such as lifting it with a helicopter) would be a logistical nightmare in that scenario. Their plans to drive on the otherwise unoccupied freeway and then circle the airport runway were much more practical.
The other glaring problem with "stopping the bus while keeping the wheels moving" is those pesky laws of physics. Momentum, kinetic energy, and inertia would all prevent that from happening under any circumstance that could be quickly cobbled together by any police department. I'm sure physicists and engineers could come up with something given a few months and a buttload of money, but for this example you could consider it impossible - especially without causing a lot of passenger injuries.