Continuity mistake: The wound on Maya's forehead changes color, angle and position through the film.
Continuity mistake: When Tony is attacked by helicopters in his Malibu mansion, his right hand has a black wrap around it. After he gets buried by rubble underwater in the suit, his right armored hand detaches and grabs his bare right hand to pull Tony out from the rubble. Tony's bare hand no longer has a black wrap.
Character mistake: When Happy is in hospital, two bad things happen: One, when a nurse comes into the room, she injects a drug into his IV line, but she doesn't kink the line above where she is injecting, so the drug goes both down and up the line. Two, Happy's IV line isn't attached to a pump. The nurse manually fiddles with the flow rate of Happy's IV. But the fiddling leads to nowhere, as she doesn't look at the chamber where the drops come out - this is very important, as the IV bag can run out anywhere from 30 mins to 3 hours.
Other mistake: Immediately before the helicopter attack on Tony's house, Maya (the "botanist") looks at the TV set, which shows a news chopper shot of the home, and says "Should we be worried about this?" It's only a moment later, when everyone looks at the screen, that a missile track appears on the screen.
Other mistake: The Miss Chattanooga Christmas Pageant should have been named "Miss Tennessee", as the pageant was made up of contestants from the various cities of Tennessee and not counties or suburbs of Chattanooga.
Visible crew/equipment: When the President boards Air Force One with the Iron Patriot you can see the reflection of the camera boom and crew in the two black cars in front of the plane moving to the left.
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.