Revealing mistake: Look for the blatantly awful special effects when the main bad guy is falling into the flames.
Continuity mistake: Admiral Bates has different ribbons from the first movie to this one. Not only does he have at least five additional ribbons (which is possible), but certain awards have disappeared altogether.
Factual error: Several of the Navy Officers seen throughout the movie, including Admiral Bates have some of their ribbons in the wrong order, to include the marksmanship ribbon and Kosovo.
Revealing mistake: When Bobby opens the door to grab the CD from the computer look at his right hand, he already has the CD before he's taken it out of the computer.
Continuity mistake: When Travis Dane went on the computer to switch tracks to begin the course for the head-on collision, the monitor displays the green trail swapping from the upper track to the lower track. In the next scene where you see the train passing over the switch track, it went on the upper track.
Continuity mistake: When Casey Ryback is heading towards the start of the train, Penn asks his henchman to check the roof of the carriage. In the first shot a man gets up off his seat and another one takes his place. In the second shot when the man is outside making his way onto the roof, you can clearly see that the other man has not moved from his position, let alone taken his place.
Continuity mistake: This happens when they stop the train in order to get the CD that was confiscated by Steven Seagal. A moment or two after the train comes to a complete stop, Travis Dane explains how important the disc is - if you look behind him you can see the scenery outside the window still moving very quickly.
Audio problem: At the beginning of the movie, the terrorists start take over the train, Ryback beats up a terrorist and throws him out of the train then some guy says something into the radio like, "we got one casualty", his mouth doesn't match what he's saying.
Revealing mistake: When Ryback is fighting the grey-haired bad guy in the kitchen, the bad guy is losing and spots a meat cleaver on the counter. When he quickly picks it up, holding it at head level, you can see the cleaver blade wobbling from side to side. An obvious rubber prop.
Factual error: The film's plot violates the third of the Ten Immutable Laws of Security by Scott Culp. The premise of the law is: When one has physical access to a computer system, given enough time, he can take over the system. In the film, the reverse happens: Dane takes over an ATAC site remotely while people inside (who have complete physical access) cannot do anything to wrest the control back. In the real world, it is usually possible to simply cut the connection cable or antenna and take control back. (Even Windows XP and later have such simple lockdown provisions as part of Windows Firewall.) After the lockdown, the passcodes can be changed and other measures taken.
Suggested correction: They don't have physical access to the satellite. It is in orbit, it is impossible to have physical access unless they had someone on the satellite.
That would be a plausible explanation, had it been in the film. But in the film, Dane hacked into ATAC system, not the satellite. That's how he implemented bogus satellites.
You also have to remember Dane designed and wrote the software that ATAC is using. He may have written in access stuff that can't be disabled. So they couldn't have disconnected the building and gotten back control of their systems. There is no way that they could have gotten back control of their satellite.
An yet, the exact opposite happened at the end of the film: Ryback shot Dane's laptop, severing his persistent remote connection. Immediately, ATAC personnel regained control of the satellite. It appears you're smarter than the filmmakers and would make a better film if you tried. But it also appears that they've made not one but several mistakes here.
Plot hole: Dane says as long as the train is moving the signal to Grazer-1 is completely transparent. So shouldn't ATAC have been able to find Grazer-1 during the ten or so minutes the train was stopped while the bad guys were looking for the CD?
Other mistake: When Ryback enters his message about the train being hijacked into his PDA he faxes it to the Mile High Cafe and signs it Ryback. When the cook at the cafe gets the fax there is no signature on it.
Plot hole: Dane's motivation for hijacking the satellite is supposedly because ATAC fired him. But he would have already had the satellite programmed to respond if he used it remotely like he does on the train except he wouldn't have known he'd be fired at the time, so he'd have no reason to have the satellite ready to hijack.
Suggested correction: Dane was a paranoid genius. There's no way that he didn't build in a back door that he could take over the system remotely.
Audio problem: When the mercenaries begin to take over the train one of them grabs an older woman and the small child with her. The bad guy threatens to "shut that bitch up or I will", but what he says doesn't match his mouth.
Plot hole: At the end of the movie once Ryback and the others take over the helicopter, Ryback calls in to ATAC to let them know the hostages were OK. How did he manage to do this? He didn't know where Admiral Bates and his people would be, only that he was able to send his fax message to his cafe, which still had no idea if his message got to Bates at all. It also begs the question how Ryback could turn a dial on a radio and magically call in to a top secret military facility that he didn't even know about.
Revealing mistake: Before Trillings and Gilder enter their passcode for the first time at ATAC there's a screen showing the codes already entered and the transfer completed before they've typed anything.
Other mistake: When Ryback enters the locomotive to search for a working radio (which he finds cut), he grabs one of the terrorists who wanders in, presses the gun to his neck, and shoots. As the guy falls away, you can see that he has no bullet hole in his neck. At such close range, all of the damage that it caused would be unmissable.
Continuity mistake: When Captain Trilling enters the room where Captain Gilder is waiting for him, she says "Have some champagne, Captain Trilling." When she says this, she has the wine glass in her right hand. A split second later, as Captain Trilling gets close to her, she has changed the glass to her left hand. There was not enough time for her to do that, especially lying on her side like she was.
Continuity mistake: When they decide to use the second Pegasus missile, the guy with the glasses says that they still have eight possibilities left. The Admiral tells him to pick one. He is about to pick Delta, then switches to Kappa. In a previous shot that shows the large screen with all of the remaining satellites, when the guy said that there were still eight left, the Kappa satellite is not there.
Continuity mistake: The 2 captains are thrown out of the train into the river under the bridge. Later on, when the shooting starts in the hostage's cars, they're back and one captain is shielding the other.