Continuity mistake: When Superman saves Lois from the car crash, the bumper's damage changes between shots: sometimes it's dangling on the edge, others it's attached to the car.
Revealing mistake: In several scenes Superman has fillings in his teeth.
Revealing mistake: When Jor-El is placing the baby Kal-El into the spacecraft, you can see his Rolex under his sleeve.
Visible crew/equipment: Just after young Clark Kent jumps in front of the train, there is a close up of the train speeding by with a very visible camera in its reflection. (00:30:00)
Continuity mistake: 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 ahead and lies next to the car; and the immaculate field is now destroyed by a huge ditch.
Visible crew/equipment: Near the beginning when Lois and Clark are walking out of the Daily Planet, Clark gets stuck in the revolving doors. But, look closely at the glass door, and you can see Richard Donner (confirmed in Superman expanded commentary) holding the door so that Christopher Reeve can get stuck.
Continuity mistake: Liz places her kitty on her right shoulder and on the next shot the cat's gone.
Revealing mistake: When Superman holds the plane's engine, the "S" on his shirt is looking the wrong way, revealing the angle was flipped.
Revealing mistake: Superman startles a cat burglar who falls from the side of a building. When Superman catches him he is facing upwards yet his cape does not fall back, it stays parallel to his body.
Continuity mistake: When the three villains get trapped by the glass, Ursa's face and haircut are totally different.
Continuity mistake: When the train is about to derail, we see a bunch of goats and donkeys under the bridge, with a kid dressed in jeans and a blue shirt, and a bearded man with a white jacket. When the shot changes, the man is wearing the kids' clothes and the boy has vanished.
Revealing mistake: When in the prison yard, Luthor's bald cap is hanging loose around his nape.
Visible crew/equipment: During the first scene in the Daily Planet, after Lois exits Perry's office saying "You forgot my report", two big stage lights get reflected on the left glass door.
Continuity mistake: When the burglar falls from the building, his flashlight is sometimes swinging, but other times it's flat against his body revealing the camera was tilted.
Continuity mistake: Near the end of the movie when Superman pulls Lois Lane out of the car and she's already dead, she is very dirty all over because of all the dirt that "drowned" her. In the following shot when Superman is done crying over her and leaves her on the ground to reverse time so that she will come to life again, her clothes are all white and shiny.
Deliberate mistake: At Lois' penthouse, before Superman says goodbye, the image is sharp and clear. Cuts to a close-up, and then check the next wide angle where he says goodnight and flies away: It's blurry and grainy because it's not live, but a screen with a previously shot scene to allow for the camera to turn left and, in a matter of seconds, no cuts at all, show Superman magically and quickly transformed into Clark Kent.
Revealing mistake: When Superman hears Lex's message, he flies all over Metropolis very close to the street, but no one reacts, revealing it was a superimposed projection and the extras were not told how to act. (01:41:45)
Continuity mistake: When the lady of Lex Luthor is in a red dress pretending to be unconscious on the road we see her legs flat on the ground, then in the next shot one leg is standing up.
Visible crew/equipment: While Lois chats with Clark and says "three kids, two cats" a microphone is reflected on a glass on the lower right corner. (01:03:50)
Answer: He wanted to see for himself if the stories were true. Some reporters tend to exaggerate the facts and if he had any other weaknesses. He couldn't be sure the kryptonite would work.
While I don't exactly disagree that Lex wanted to see for himself how invincible Superman is, I don't think that's the main reason why he did it. The bullets and fire were simply a charade to make it look like this was his security system. Keep in mind, he wanted Superman to enter his lair because the real trap was the Kryptonite that he had in the lead box.
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