Secret Service Director Jacobs states that the activation of the ICBM self-destruction program--which does not exist--would make the U.S. vulnerable to nuclear missile attack. Reality is that the ICBM, SLBM, and bomber force only deters such an attack...the nation has always been vulnerable to nuclear missile attack, as it does not have a deployed, large-scale missile defense system (and did not pursue one under the ABM Treaty with the USSR/Russia).
After Banning and Connor emerge from between the walls, Banning shoots his pistol to slide lock. He immediately drops the pistol and draws another. But the next shot shows him still holding the empty pistol.
When Banning's wife is watching the news with other medical staff on the TV, the white coat of one of the staff members carries the logo for North Louisiana Hospital, even though they are supposed to be in Washington. (Many scenes were filmed in Louisiana).
Both planes sent to intercept the intruding Gunship are shot down by Gatling guns mounted on each side of the enemy aircraft. To avoid incidents like this all interceptor fighters use special intercept-formations where one plane establishes visual contact with the intruder, thus flies beside him and the other one flies behind the intruder to shoot him down, should the other interceptor experience hostile action.
There is no Cerberus code or other self-destruct capability on U.S. nuclear missiles. Also, the possession of one of the codes by the Chairman of the Joints Chiefs of Staff would make no sense. The Chairman is not the chain of command for the employment of nuclear forces. The President, the Secretary of Defense, and the Commander, U.S. Strategic Command (who is stationed at Offutt AFB, Nebraska) are the "top three" in this chain.
The C-130 evades the SAMs launched from the White House by emitting flares. In reality, this tactic would be useless. The SAM batteries installed on the rooftops surrounding the White House (not on it) are the Norwegian Advanced Surface to Air Missile System missiles, which use both a monopulse Doppler tracking radar and a laser beam to guide the missile to its target. Flares would have had absolutely no effect on the missiles.
The non-existent self-destruction program which exists on the ICBM force is shown all over the U.S. map. In fact, the 450 U.S. ICBMs are based out of Montana, Wyoming, and North Dakota, with missiles in each of these states plus Colorado only.
All references to NORAD are incorrect. NORAD (the North American Aerospace Defense Command) is a combined command with the mission of detecting and reporting attack on North America. It possesses no nuclear weapons. The combatant command responsible for strategic attack is Strategic Command, and the ICBMs would be operated by the Air Force Global Strike Command, not NORAD.
The Presidential limousine has standard thickness doors and windows, revealing it has not been reinforced with armor plating and ballistic glass. The actual Presidential limousine is so heavily armored, the Secret Service refers to it as "The Beast."
(at around 81 mins) The drone that spots incoming helicopters is the small, electrically powered drone that was launched at dusk (around 7pm). It does not have the power to remain in flight for 4+ hours.
When the AC-130 is intercepted by two USAF aircraft right before the attack, they are both shot down after the AC-130 deploys cannon on both flanks. In reality, all AC-130 variants have cannon only on the port (left) side of the aircraft. The aircraft attacks by performing a left-hand pylon turn centered on its target. It is intended as an air-to-ground weapon system, not air-to-air.
When we see one of the news channels broadcasting the event, the news title reads "Terrorist Attack The White House" (instead of "Terrorists Attack The White House" or "Terrorist Attack on The White House").
During the attack, the Speaker of the House is "officially" placed under Secret Service protection because the President and Vice President are incapacitated. However The Speaker of the House is a role that already qualifies for such protection.
At about 1 hour in, when Banning discovers the President's son in the walls, the kid is hiding as he knows people are after him - yet when the glare of a flashlight attached to a gun blinds him in the face such that he has no idea who is behind it, he jumps into the arms of person with the gun. At that time he had no idea whether this was Banning or a terrorist.