Mark Valley's character FBI Agent Mike Johanssen appeared in the showdown between Agent Hubbard and General Devereaux (behind General Deveraux). However, Agent Johanssen was killed in an earlier scene at the 1 Federal Plaza bombing.
When Devereaux speaks on live TV about imposing martial law, he is speaking from New York in broad daylight. Yet, within the same scene, a "live" broadcast of Devereaux's speech is shown on a giant screen from Times Square, also in New York, and yet it is night there.
During the standoff between Gen. Devereaux and Hub the General initially does not stand down, but calls out "Captain", which is the signal for the army personnel to raise their weapons. After Hub convinces the General to stand down Devereaux calls out not to the Captain, but to the Sergeant to lower his weapon.
When the pizza box is delivered to the cell in the apartment, it is clearly sealed, with all three sides tucked in. When the terrorist places the box on the table and carries on a conversation with the other terrorists, the side flaps on the box are clearly untucked as if the box had been opened, but yet the man never opened the box until it exploded.
When Hubbard gets a nose bleed while briefing the FBI agents his tie is long and hangs well below his belt. In the next shot it is shorter and shaped differently, and then back to being long in the following shot.
In one scene before the bus explodes, Hub and Frank are driving in a car and Elise / Sharon is sitting on the rear seat. During the shots in which she is shown, you can clearly see through the rear window that the following cars are changing between shots.
At the end of the movie when Samir shoots Sharon, it is very clear that he shoots her in the middle of her chest; however, when they call the ambulance and switch the camera angle, the hole has moved down to her stomach.
At the end when Sharon and Samir are in the bathhouse, Samir removes a towel from a clay pot and sets it on the floor in order to remove the bomb. As he does so he knocks over a brass jug. Throughout the rest of the scene the jug is upright even though no-one touched it.
Twice, General Devereaux refers to "the president invoking the War Powers Act." The WPA is not presidential authority for allow war or the use of the military (which comes from Congress), but it is in fact a rule passed by Congress in 1973 (after Vietnam) that severely limits a president's ability to unilaterally use military force without Congressional authorization.
At the strategy meeting, one of the participants cites Lincoln's suspension of Habeas Corpus in 1862. Another states that this act was declared unconstitutional by the Supreme Court and cites the case "Ex Parte Milligan." The actual case for this incident is "Ex Parte Merryman." The Milligan case involved the military trial of a civilian. The case determined that civilians cannot be tried in military courts, except under specific circumstances, which the Milligan case did not meet.
The goof item below may give away important plot points.
When Hub reads General Devereaux his rights he interrupts the correct terms, in the presence of many witnesses, with a diatribe of personal opinion. This is strictly against procedure in most jurisdictions, however it is not a valid error to claim improper arrest as previously stated. Miranda warnings are only required if questioning a suspect about the alleged crime.