In the second to last scene when Alex is speaking with the First Lady, the line of blood from the cut on the side of his face goes up and down.
When Alex gets into his SUV on a one way street, he gets in on the right side of the car and the steering wheel is on the right side of the car. Later he is seen in the same SUV driving on the left side of the car again.
The Mammoths logo on the TV motion graphic has the tusks pointing to the left. The Mammoths logos on Thomas' displays of checks has the tusks pointing to the right. Such a logo would not be used both ways.
The bubbles from the scuba tank (the exhaled air) do not come up when the tank is being used and they do not appear until they use it as a decoy, with the air being released by itself, which would have emptied the tank. Then a day or two later, Crawford finds the tank and uses it.
When the doctor tells the First Lady that the president is dead, she asks him to tell the press. The Vice-president would have been notified before the press was informed.
Thomas drowns, then Crawford miraculously uses the scuba tank to revive him, even though his lungs are full of water.
Even though he's had a .45 hole in his left hand Thomas continues to use the hand throughout the film. Even though no bones were hit, the damage to the hand and the effects of the healing process would have made this exceedingly difficult.
The Thomas S. Foley Federal Courthouse is in Spokane, Washington, not in the vicinity of Washington, D.C. By allowing the full name of the courthouse to be in view, this gives away the actual location.
In the opening credits, Cuba Gooding, Jr.'s name is written as "Cuba Gooding, J.R."
As a freelance journalist, Crawford strongly relies on her cell phone. She would clearly carry a charger in her purse. She hears the battery alert twice, plus the call drops from a lack of power yet she never plugs in the charger. Considering the significance of what was going on, she would never have neglected her phone. Then, when the power goes out, Crawford is not in the least suspicious and even hums a little song.
The agent on fire would have known to stop, drop and roll. At one point Thomas waves a blanket at the flames, which would have provided the fire with more oxygen. Further, when the agent is yelling at Thomas the fire retardant gel is glaringly apparent.
During the general's talk with Thomas and Crawford, he spends the entire time looking down, as if he were reading cue cards, rather than looking at the two and reciting information that he knew quite well.
At several points Thomas and other agents are shown entering dark areas while being brightly backlit, which make them to be excellent targets, and when Thomas enters the dark office he makes no attempt to turn on the lights while he and his fellow agent are well lit. As a firefight was already in progress, there would be no reason to leave the lights out.
When Thomas and Crawford discover the key to the mystery Thomas makes two calls to a colleague but at no point tells him his suspicion.
When they are in the helicopter taking the president to the hospital, they say he has a "gunshot wound to the head", but in the shooting you can see clearly the gunshot was not in the head.