Continuity mistake: Ray comes to Buck's hotel room with the stolen disk containing the revised speech. At the shot when Buck is sitting at the computer reading the speech, he has a wedding ring on. Buck isn't married.
Continuity mistake: When Buck and Chloe are at the airport taking photos in the little booth, the poses that they are doing when the pictures are taken are not the photos that they end up with once they are developed.
Continuity mistake: When Carpathia is announcing he will be the president of the United Nations, you hear camera's clicking and see flashbulbs. However you will hear flashbulbs without seeing the actual flashes and see flashes without any camerasound.