In the opening scene, one of the intelligence agents examining the satellite photo confirms that there are '2 CVE's' (escort aircraft carriers), and '4 destroyers' in the Indian battle group. But in the situation room, the type and numbers of ships are flip-flopped, and the Chief of Staff reporting to the president says it's reported as '4 CVE's and '2 destroyers' (a rather large discrepancy given the circumstances).
When Charlie is talking to the President about taking his daughter out on a date Charlie's name tag is under his tie. In the next shot it is on top of his tie, and one shot later it is back under his tie.
In the opening scene, it shows the action taking place at the Pentagon. Out of the window behind the actors, you can clearly see the Washington Monument with the Lincoln Memorial behind it. This view is not possible from the Pentagon.
The map in the Situation Room labels Pakistani-controlled Kashmir as "Jamu" [sic] and Indian-controlled Kashmir as "Kashmir". In actuality, the Pakistani-controlled region is composed of "Azad Kashmir" on the west and the "Northern Areas" to the north, whereas the Indian-controlled territory is the Indian state of "Jammu and Kashmir." ("Jammu" has 2 M's in it.)
CJ describes Lord John Marbury as an earl. This is impossible, as the title "Lord John" indicates that he is the younger son of either a duke or a marquis. Leo also calls him "Lord Marbury" which is incorrect if he is Lord John; "Lord Marbury" would be used to address him if he were a baron or a peer (a peer is a nobleman of the rank of earl or higher).
Repeatedly, as in the title, we are told that the former British ambassador to India is named "Lord John Marbury," but C.J. tells someone on the phone on background that Marbury is an hereditary earl. If he is an earl, he would be "Lord Marbury," or "John, Lord Marbury," but not "Lord John Marbury," which is the form of title of younger son of a nobleman, not the holder of a title such as earl.
Director of Central Intelligence informs the President that the "KH Superplatform" has been ordered into a stationary orbit over the northern subcontinent. There is only one stationary orbit, the GEO or Geosynchrous Stationary orbit with a semimajoral axis of about 42 000 km directly above the equator. The satellite can be parked at a specific longitude and can generally not be moved from that position. Satellite tasking is not done lightly and takes time as it uses on-board consumables. Photo-surveillance satellites are generally placed in elliptic LOE (Low Earth Orbit) (orbiting 150 - 500 km above the surface) at high inclinations (around 90 degrees) thus almost polar orbits. GEO is a circular orbit. Thus it is impossible to have live coverage of an area for long time. In order to obtain photographic surveillance on short notice reconnaissance aircraft are employed (if possible).