Revealing mistake: One of the Air Force One survivors is shown floating awkwardly on his stomach with his legs in the air. This was due to the floatation device used by the actor, because no unaided human would be able to be so buoyant in a pose like that. (01:37:00)
Revealing mistake: When Tony and Rhodes are on the oil tanker bunkered behind an obstacle, Tony realises his gun is empty and asks Rhodes for a new magazine. When Tony ejects the magazine you can see that it is actually an airsoft gun magazine; thus exposing that it is actually a prop gun.
Revealing mistake: When Tony is knocked violently forwards during the test of the Mark 42 armour, he somehow arrests his fall mid-air just before propulsors in his hands actually fire, because the effects weren't perfectly synced with the wirework.
Chosen answer: The Battle of New York was never specified to take place in 2012, we just know that the film came out then. Based on the newspaper we can assume that the battle was in June 2013, rather than some time in 2012 as many would have previously assumed.