Plot hole: The fact that a five minute timer starts after the three Cerberus codes are entered defeats the purpose of the program. If they program was made to destroy their own nuke warheads in case of a misfire you would expect them to be destroyed as soon as all three codes are in. (01:38:20)
Factual error: Near the finale, Kang sends a command to all US based missiles to self-destruct in their silos, thereby detonating their warheads. Ignoring for the moment why "self-destruct in silo" would ever be a desirable scenario programmed into ICBM protocols, detonation of a nuclear warhead requires an extremely precise sequence of events, none of which would include a nearby, conventional explosion. (01:38:20)
Factual error: When one of the terrorists fires an RPG into the security hut, all the windows in the cars standing nearby shatter. Ordinary windshields are made of laminated glass that doesn't shatter, not to mention that at least the SUVs used to transport the prime minister and his escort would surely be armored and therefore possess security glass. (00:28:20)
Other mistake: At the end of the movie, when the president gives a speech, Mike Banning's face still shows the unhealed cuts from his fights at the White House, suggesting that this is only a couple of days or so after the event. However, the President, who was shot in the gut and on the verge of dying, is completely recovered.
Character mistake: When the main characters are watching the news on TV, the headline reads "Terrorist seize Whitehouse". It should be "Terrorists".
Factual error: When the AC-130 gunship flies over the White House, some of the Secret Service agents on the roof are firing bolt-action sniper rifles without pulling the bolt back, like a semi-automatic gun. (00:25:20)
Continuity mistake: Towards the end of the movie as the Marines are once again raising the flag on the White House after the terror attack you can see that the roof is still brutally damaged and there has been no repair work done. When the camera pans over toward the Washington monument, you can see that the monument is already being reconstructed with scaffolding all around it. (01:45:30)
Continuity mistake: When a woman is shot in the head, the bullet hole is in the left side of her hat. But then when her hat falls off, the bullet hole is in the right side of her head. No, the bullet didn't pass through both sides. She was shot from the front, so there should only be one bullet hole in the same place. (00:30:00)
Factual error: The Secret Service has more than 3,000 Special Agents across multiple government organizations. Other than those who work the White House and Presidential Detail, it is highly unlikely that others would have any White House access, much less current security codes, as Mike does. Agents would not have passwords to the President's laptop - but Mike is able to log in and delete all the classified data on it.
Factual error: Toward the end of the movie, when the US 7th fleet is ordered to withdraw from the Sea of Japan, two US aircraft carriers are shown maneuvering. One has '67' painted on its island, the other displays '73'. This represents the hull number of the ship. CV-67, the USS John F Kennedy, was decommissioned in 2007, and the F-14 Tomcats on the carriers' decks were retired in 2006.
Visible crew/equipment: When Banning is collecting guns just after the power goes out, he kills one terrorist in an orange top. When crouches down to pick the gun up, the whole place is in darkness. As he stands up a round white light is reflected in a picture on the wall behind him. (00:41:05)
Factual error: In the operations room from which the acting president (Morgan Freeman) is directing the crisis there are multiple uniformed military members at the table and seated on chairs behind the acting president. Over Morgan Freeman's left shoulder is seated a man wearing the uniform of an Air Force Senior Enlisted member (can't quite make out of the entire rank, probably a Chief Master Sergeant). The person portraying the Chief is way too old for the rank. On the other hand, a three-star Air Force General is depicted at the conference table and the actor is way too young to have three stars.