Scenes take place in an underground parking garage at The Penatgon. All parking is above ground there, in several large lots, to avoid car bombs damaging the building.
When Mac Casey meets Sarah McCann in the plaza, we hear the band playing the "Liberty Bell March" but the conductor is obviously directing a much slower piece of music.
Numerous scenes were clearly filmed in Southern California, not Washington DC. For example, the city skyline shown more than once is that of L.A. Also, you can see a Canary Island Date Palm (which would die in D.C.'s winters) along the road during a military convoy.
Near the beginning, Forrest Whitaker is looking at a computer screen showing military bases. On the list is Fort Bragg, CA (actually in NC) and Boluxi, MS (should be Biloxi).
The entire premise of the Presidential takeover in the film implies that the moment the Cabinet members and the Vice President declare the president unfit for duty, he will be removed from office. However, Section 4 of the 25th Amendment outlines a detailed procedure for the manner in which a President may appeal a declaration that he is incompetent. The procedures specifies that the Vice President and the Cabinet may then re-state their case, in which afterwards the matter is forwarded to Congress. The stipulations of the 25th Amendment are in place to prevent exactly the type of scenario which is shown in the film.