Deliberate mistake: In the scene where they break into the train from its roof, you can notice that despite the high speed and the consistent wind, Captain America's fellows have no difficulties in running, standing up still, and even jumping, like they felt no air resistance. Moreover, you can see that their hair is not moving at all, completely missing to realize any "windy" effect.
Deliberate mistake: Right at the end of the film, the two Norwegians (Lars and Matias) are seen chasing after Lars' dog in a helicopter. Notice how their clothing and the interior of the helicopter are not the same as they looked in the original 1982 film by John Carpenter. It's supposed to be the same event.
Deliberate mistake: The scenes involving the 8mm projector and screen did not also contain legitimate light rays from the projector to screen or show any obstructions on the screen despite Joe or someone else between the projector and screen. What showed on the screen is what would be expected if using a videotape or DVD.
Deliberate mistake: This mistake was admitted to in the DVD commentary by the director. When at the embassy, once they open the window, the camera pans up to show a destroyed helicopter on top of the building. This is a mistake as in Moscow, it is restricted airspace for helicopters, with none at all for any purpose to be allowed to fly over the city, not even to land on the American Embassy. However, the director really wanted the visual of a destroyed helicopter on top of the building so added it anyway. (00:41:49)
Deliberate mistake: When C-3PO, R2-D2 and the younglings are driving through the battle zone, Anakin Skywalker and General Grevious can be seen battling. Later, Darth Vader can be seen on Hoth. This would be impossible due to Anakin Skywalker being Darth Vader. (00:08:50 - 00:12:20)