Factual error: Never mind that their faces are taken off (and a fast recovery time, as well), but John Travolta is tall with broad shoulders, Nick Cage is short and thin - how did all this get changed? I know plastic surgery is possible, but these two men would need intensive plastic surgery and would need months or years to recover, not several hours.
Other mistake: At the prison, when Sean Archer (as Castor Troy) is talking to Pollux Troy to find out where the bomb is, Pollux hands him a cigarette. Never lighting the cigarette, in the next shot the cigarette is lit and he is smoking from it.
Continuity mistake: In the boat scene when the white boat crashes through the police boat you can see the front of the white boat shatter and then it's okay again.
Continuity mistake: When John Travolta is shot on the carousel at the beginning of the movie, the shot enters his back near his collarbone. When the camera moves back a second later, the bullethole is much lower.
Factual error: In reality, a face transplant like this couldn't work for multiple reasons. Primarily because of blood type, with Castor (Cage) being AB and Sean (Travolta) being O Negative. Organ donors and recipients need to have the same exact blood type for transplants to work, otherwise the recipient's body will reject it even with medication. In addition, intensive surgery is needed to connect a donor face to a recipient (ex. Connect blood vessels), which takes more than several hours.
Continuity mistake: In the shoot-out sequence in the Mexican Standoff scene between Archer, Castor, Sasha, Eve, and Castor's two bodyguards, you don't need to look carefully to see that the exact same footage is used twice at different times to show a flowerpot exploding. Also, a bad guy gets shot and falls the exact same way twice at different times. He doesn't even fall at a different camera or body angle.
Continuity mistake: When Castor Troy first arrives at the airplane you see another business jet in the back (you see the red engine coverages). Few seconds later there is a different aircraft with a propeller and no jet anymore.
Revealing mistake: When Cage is shooting Travolta with the Uzi type weapon in the room with mirrors, the gun has no muzzle flash in several shots.
Continuity mistake: Towards the end of the boat chase, the "Coast Guard" boat is facing towards the two boats. A few seconds later one of the chase boats flies through the Coast Guard boat from its rear. It would have taken too much time to spin that boat around for the boat to crash through the back. And even if it were possible, most of the crew were shot and fell off the boat. Who drove the boat to position it for the crash?
Continuity mistake: Castor Troy puts three bullet holes in the windscreen of the helicopter Sean Archer is in at the start of the movie. When Archer moves toward the hangar to shoot Castor, you can see in the background that there are now no holes.
Visible crew/equipment: When Pollux falls through the glass roof, you can see his harness pulling him back.
Chosen answer: It's obvious that enough time hasn't passed for a trial of such magnitude to take place, meaning that the brothers have been remanded in custody to await trial. They should have been arraigned but we don't see that onscreen.