Other mistake: At the end of the first movie Rybak is a Chief (E7), and he is a retired Lieutenant (O3) during this movie. Assuming he got commissioned to Ensign (O1) immediately after the events of Under Siege, it would take a minimum of 42 months to be promoted to Lieutenant. This movie takes place within 4 years of the first movie, because Admiral Bates is still the Chairman of the Joint Chiefs of Staff. The picture of Rybak in his Lieutenant uniform is at least 5 years old according to his niece. None of these timelines make sense for the rank he is in the movie.
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?
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.
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.
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.
