The movie also appeared blissfully unaware that the US posseses aircraft like Apaches and AC10s that can engage targets from literally several miles away. I also like the White Houses's anti-aircraft missile defense system that causes attacking aircraft to crash and burn into the White House, thereby solving nothing and rendering it pointless.
More than just that. Allow me to list some issues:
* The two fighters fly on both sides of the C-130 at the beginning, allowing its Gatling guns to destroy them. The actual procedure in real life involves ONE fighter flying next to it and the other flying behind it, specifically to prevent this from happening and allow for the bandit to be shot down if it's hostile.
* The Chairman of the Joint Chiefs of Staff isn't part of the chain of command for the nuclear launch codes. The third person would be the Commander, US Strategic Command at Offutt Air Force Base in Nebraska.
* Not only is there obviously no ridiculous mass self-destruct system for the nukes that could be activated while the missiles are unlaunched, it certainly wouldn't cause any kind of nuclear holocaust that evaporates America. Nuclear devices require an extremely specific sequence of events within the warhead to create the exact situation needed for the chain reaction that causes a nuclear explosion. If anything goes wrong or gets changed (such as from being blown up), the warhead is disabled. It certainly wouldn't be a good thing to self-destruct an ICBM in its underground silo (along with the damage from the explosion, it would throw radioactive material around, though the underground concrete silo would shield the surroundings from the brunt of the damage anyway), but it would hardly nuke the surrounding area.
* Speaker Trumbull (Morgan Freeman) did one of the absolute worst jobs of anyone potentially given command: he gave in to almost every one of Kang's demands, gave the order to pull all troops out of Korea in a move that would freely allow the Korean War to reignite, and allowed Kang to freely kidnap the entire surviving Cabinet and take them all to wherever he desired....all in the name of not letting the President and the rest of the Cabinet get assassinated. Congratulations, you fucked it all up.
* Kang is one of the most wanted terrorists in the world. His disguise? A pair of glasses. While traveling as the South Korean Prime Minister's head of security. I know there are stories about wanted criminals working as janitors or cafeteria workers in the Pentagon or FBI office or whatever, but those are civilian jobs that slip under the radar. Did South Korea just select their security detail through pulling a name out of a hat before the trip?
* Kang is an independent terrorist, not a North Korean agent. How exactly did he get an army of followers with modern military weapons, a C-130 fitted with M134 miniguns, a disguised garbage truck with M240 machine guns, and large amounts of explosives and brilliant computer hackers? I mentioned this on the TV Tropes page, but it's a film that relies on Kang being fabulously wealthy and hypercompetent.
* Also something I mentioned on TV Tropes is that the entire Western military and security detail has the tactical capability and accuracy of amateur airsoft players. There's an extended sequence where not only do a ton of Secret Service agents run out the door and get slaughtered by the M240s, but they
keep running into the line of fire blindly. It's like watching Soviet conscripts being forced over the top to swarm machine gun nests and flies in the face of literally every piece of modern combat training. During the fighting in the White House, they make dramatic spins around corners while sneaking around by themselves, with absolutely zero attempt at coordination, and get shot almost immediately. I have literally displayed better tactical thinking when playing airsoft than what is depicted in the movie.