Other mistake: This error occurs during the scene in which the President and Lewis Rothschild are riding in the limo, just after the President has broken a date with Syndney. The background scenery, visible through the windows of the car, is noticeably in slow motion, even though the car (and the people inside it) are moving at regular speed.
Other mistake: The scene showing the Capitol Building is a still shot. There are birds flying in front of this scene, but the water and birds actually in the scene aren't moving.
Answer: The aria is "Viens, Mallika" from "Lakmé", composed by Léo Delibes.
scwilliam