Timmy Hanson says "being the vice president is better than being the president...'cause nobody wants to shoot the vice president." That isn't quite true. In 1804 sitting vice president Aaron Burr infamously dueled against former secretary of the treasury, Alexander Hamilton. Hamilton's shot missed Burr while Burr's shot mortally wounded Hamilton, who died the next day. Burr was later tried for murder but acquitted. However, the character who says this is six years old, and probably does not have such an extensive history knowledge.
In the yacht scene, a close-up of the President's West Point Ring can be seen. This reveals the Academy Crest facing away from the heart (as if saluting). Upon Graduation from West Point, graduates face the Class Crest away from the heart and the Academy Crest towards the heart.
Near the end of the movie when the President is walking onto the podium to give his speech to Congress, the camera pans across the back of the Assistant Cameraman wearing a gray ball cap and holding the remote focus device for the camera.
When Runyon and Webster are speaking for the first time, they pass a room in which a chandelier that appears to have a black flag (a piece of grip equipment used to block glare from lights) attached to it.
When the Senator is going with her husband to meet the President for the first time, the Lincoln Memorial is clearly seen is the back window of the limo, indicating that they are leaving DC on the Memorial bridge, heading in the wrong direction.
Senator Hanson is seen jogging in what is undoubtedly meant to be Arlington National Cemetery. Jogging is not permitted in Arlington National Cemetery, and presumably a U.S. Senator would know better than to be seen disrespecting American veterans in such a way.
Towards the end of the movie when the President is addressing Congress, Joan Allen is seen outside of the building jogging. Joan Allen, being a senator and therefore a part of Congress, should have been inside the building.