Continuity: When Captain America is found in the ice he is in a spread eagle position. In the next scene when he is unloaded out of the transport (still encased in ice), he is perfectly straight.

Factual error: General Fury incorrectly uses the DEFCON System. When all of S.H.I.E.L.D's secrets are revealed to the Chitauris, Fury moves to DEFCON 4, which is peacetime with increased intelligence and security. When the threat increases and Chitauri ships are approaching, Fury moves to DEFCON 5, which indicates peacetime. In the DEFCON system, lower numbers indicate higher threats.

Continuity: In the scene where Thor hits Hulk with his hammer, he swings it, but in the next shot it shows him with his arm extended as if he hit him with his fist.