When discussing his grand plans, Lex Luthor makes a throw-away line and names a country to be blown up apparently at random. Not quite so random - it was changed in each country of release. See more...
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Continuity: Kal-El's cradle arrives on earth, flies zooming past the Kents' car, which is driving in the opposite direction and crashes 500 meters behind the vehicle. The car keeps moving for about 200 meters and then pulls over. A brief shot shows an intact curb on the right. However, when Jonathan Kent gets out of the car, everything changes: The cradle has moved 700 meters and lays next to the car; and the immaculate field is now destroyed by a huge ditch.
Revealing: 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.
Continuity: When leaving the Daily Planet for the first time together Clark gets stuck in the revolving door behind Lois. He lets her go through ahead of him and gets in the next section as the door revolves. Cut to the exterior of the Planet when they emerge (just before they meet Rex Reed) and Clark is in the same section of the revolving door as Lois.
Character mistake: In the Air Force One scene, when lightning destroys one of the plane's engines, one of the pilots tells a co-pilot to inform Metropolis Airport that the president is on board the plane. The crew is unnecessarily repeating themselves: just a few moments before, they radioed in that "Air Force One" was on approach; the plane would only have that call sign if the president was on board.