The President sends a B-2 Spirit bomber, however when shown the bomber is definitely a F-117A Nighthawk Stealth Fighter
The crew of the B-2 that the President wants to speak directly to are identified as "commanders", a US Navy rank; only the US Air Force operates the B-2, and the USAF does not have a rank of "commander".
The nuclear football is carried in rotation between the services, in the film its stated that the Air Force carries it. The football contains a card with launch codes, an identifier device, a computer with launch capabilities and a keyboard. It is twice the size of the one in the film.
B-2 bombers are based at Whiteman Air Force Base in Missouri. It wouldn't make sense to base them in Saudi Arabia since they have the range to reach Iraq from Missouri and it would put them in danger by placing them in range of enemies such as the Iraqis.
The National Security Advisor refers to the South Korean leader as a premier. South Korea doesn't have a premier, it has a prime minister. Even then the prime minister is pretty much a low importance office, with the real power held by the South Korean president.
The president stated that a 100 megaton bomb was dropped on Baghdad, but this impossible. The largest nuclear weapon ever detonated was 50 megatons, the famous Tsar bomb. The are no weapons in the US arsenal even close to 100 megatons. The largest detonation of a nuclear weapon by the US was the Castle Bravo test, with a yield of 15 megatons. This detonation was not intentional however, but the result of a runaway reaction. The fact that the president in the movie had reduced the US arsenal further makes this scenario unlikely.
Katie comes out from behind the counter carrying a supposedly hot coffee pot, intending to "warm up" the coffee of the people around the counter. Unfortunately, she carries the coffee pot by both the handle and with her right hand on the glass bottom and side.
The news shows footage of "Iraqi" forces, but they're actually U.S. forces upon closer inspection.
The code for the briefcase is 08061945. This 'code' is also the date where the US dropped the bomb on Hiroshima.
The National Security Advisor, Gayle Redford, argued against the dropping of an "Atomic Bomb". A person in her position would never have used the term "Atomic Bomb" in 2007. The US nuclear arsenal was converted entirely from Atomic to Hydrogen Bombs in the 1960s.
There are ships visible at the base of the mushroom cloud that is supposed to be at Bahgdad.