Revealing mistake: When Tony is having his first fight in the embassy, it is obvious that most of his punches do not connect at all. The people he supposedly hit still react as though being hit, and the sound effects of a fist hitting a jaw are still there, even if Tony misses by several inches.
Revealing mistake: When Dana is walking down one hall with Leroy and a bottle of champagne, the exit sign is reversed. (00:53:05)
Revealing mistake: In the big speedboat scene near the end, when Cage is hanging off the side of the boat the stunt double is obvious in wide shots, where the entire boat is visible from above. He has big long sideburns, which are in stark contrast to Cage's short hair, visible in closer shots. At various other points in the movie, stunt doubles appear of much different physical builds than the two actors, with markedly different hair colours, and I seem to recall that at least one of them had facial hair.
Revealing mistake: Aeon's neck freckle swaps sides in one shot, revealing a flipped shot.
Revealing mistake: When Ellie is traveling through space, she unbuckles herself from the chair to retrieve the compass. The chair then breaks off from the violent movements of the space pod, and slams up against the ceiling. At this moment, Ellie is in deep space in a completely weightless environment. She is floating, suspended in the pod and the chair itself floats a bit before being slammed upwards by the force of the pod movement. But, some small parts of the chair (bolts, etc.) are seen falling directly down, towards us in obvious full gravity; revealing that the scene was actually shot in normal gravity.
Revealing mistake: On Miranda there is a shuttle crashed into the side of a building, but there are no burn marks or a trail from where it had crash landed. The shuttle couldn't possibly have crashed into the building horizontally without crashing diagonally/vertically first, landing horizontally and then sliding into the building. Joss Whedon even states in the director's commentary that some burn marks would have been nice but it only occurred to him about 14 months after it was filmed. (01:17:15)
Revealing mistake: During the scene where the military loses control of London, and their snipers are told "all targets are free", you can see heavy padding beneath Infected/civilian victims' shirts, etc, as they're shot. Presumably it's to stop them injuring themselves when they fall over, or to hold apparatus for the blood effects, but it's too bulky to be part of the characters' clothing.
Revealing mistake: When David is sitting in L.E. at the end and the camera is zooming in on his face his mask changes. In the very last shot of him just about to pull it off it's much wider/looser so it'll come off easier.
Revealing mistake: When they are climbing up from the subway tunnel into Madison Square Garden, there are lots of half-dead fish scattered around from when Godzilla was feeding. Right before they enter the arena, in the overhead shot looking down on the actors, there is a wiggling fish in the lower left portion of the screen. If you look closely, you can see a string attached to the fish. A crew member is obviously tugging on it from below, to make the fish move.
Revealing mistake: In the parking garage shoot out Arnold shoots the leg off a bad guy. While the bad guy is writhing in pain on the ground you can see his leg tucked back. (00:59:50)