Revealing mistake: In the final scene, Superman is returning the White House's flag to its rightful place, flying over the fountain on the lawn...which is frozen solid in place. Obviously a photo backdrop.
Revealing mistake: When Zod lifts the boy's father with the beam of white energy, watch closely when he raises him up past the telephone pole...he 'clips' right through it, or rather the pole clips through him, as if he is transparent.
Revealing mistake: In the beginning, when Superman is flying to the Eiffel Tower, the last scene that shows him flying towards the tower, you can see the wire Christopher Reeve was attached to as he swoops down. The wire stretches all the way across as Superman glides down.
Revealing mistake: When Zod says to Ursa to "blow them a kiss my dear" to the helicopter that's firing on them watch as the helicopter is indeed a real military helicopter, then when it loses control it's an obvious model and just before it crashes into the house it's a full size helicopter again but is completely different from the first one that was originally shown.
Revealing mistake: In Houston, when a man is thrown through a truck, notice the ground he falls on: The sand is leveled higher than the rest of the road around, obviously to hide a landing mat. Furthermore, after the fall the man turns around and he's got a bulgy square on the back to help for a safe stunt.