Revealing mistake: When Lois is at the heliport, watch the wind flag on the left: when the helicopter arrives, the roaring wind from the vanes makes the flag move up and get stiff. In the close-ups, you keep on hearing the sound but the vanes are off screen. Watch and you'll see the wind flag is down, thus revealing that the engine is off and that the sound we are hearing is fake.
Revealing mistake: When Otis first arrives in Luthor's lair beneath the train station, he knocks a table lamp over. When the lamp shade comes off the lamp, the bright, exposed light bulb then dims to a less-distracting level for filming purposes. Otis then replaces the shade upon the lamp, and the bulb then instantly goes back to its original level of brightness, so that it will look appropriately illuminated through the shade. The bulb's brightness was manipulated off-screen to conform with the needs of the bulb's effect on the scene.
Revealing mistake: Superman has just saved Jimmy at the dam and is holding him in the air. Jimmy's fringe is standing up thanks to some hair fixer to achieve the effect of wind blowing (though it's a green screen effect). When Superman sets him on the floor his hair remains up giving away the trick, until the angle changes and it looks all combed and nice.