Continuity mistake: At the beginning when Jor-El and the council pass judgement on the three criminals and the huge white dome starts to open, it stops about a third of the way. Long shot of the three criminals, it's completely open. Next shot it's back to a third of the way open.
Continuity mistake: In the football field, all the player pass in front of Clark and leave him alone. In the next angle a player is passing by again.
Continuity mistake: At the police station, behind the fat cop there's a young cop picking up papers who walks to the left and stays there for a while. When the angle changes he reappears in the previous spot, repeating all the movements.
Continuity mistake: When Luthor switches the snow machine off, a wide angle shows the chamber totally covered in snow and ice, but the close-up of the vents and the walls surrounding are spotless.
Revealing mistake: When Superman holds the plane's engine, the "S" on his shirt is looking the wrong way, revealing the angle was flipped.
Continuity mistake: During the Golden Gate Bridge crash sequence, a reversed shot of a life-sized 1972 Trans-Am braking hard is shown. The next shot shows a model car smashing into a model school bus, and the car is suddenly a 1965 Corvette. The fimakers have painted it red & white so it resembles the Trans Am. (Timecode is for Director's Cut) (02:09:10)
Other mistake: When the camera pulls back from Superman in his Fortress of Solitude, right after the image of his father wanting to hug him disappears, you can see on the right of the screen that one of Superman's 'crystal' walls is fluttering or shaking like it's made of plastic.
Continuity mistake: When Ms. Teschmaker rests her arm on the file cabinet, a white roll of paper appears and disappears.
Continuity mistake: Right before Superman catches the burglar, he is standing in a steel intersection of the building. A second afterwards, he is in the middle of a window pane.
Continuity mistake: Before Superman lands on the sidewalk looking for Luthor, the aerial view shows no cars around. When he lands, the place is jammed.
Continuity mistake: When the Hollywood sign is falling on the girls, a close view shows a girl very close to a letter while her friends run away. A split second later, from a wide angle, the girl has disappeared.
Continuity mistake: When the three villains get trapped by the glass, Ursa's face and haircut are totally different.
Revealing mistake: In the shot of Krypton exploding, you can see creases in the black backdrop in the lower, left hand quadrant of the screen (especially visible on Blu-Ray).
Revealing mistake: In the final shot of the destruction of Krypton several of the people falling into the abyss disappear a split second before the shot of Krypton exploding.
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.
Continuity mistake: Lois leaves the gas station but the reflection of the glass shows it still there.
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: At the heliport, a cork bulletin board on the wall appears and disappears between shots.
Continuity mistake: When Lois is about to ride on the helicopter, there's a man in the background easy noticeable because he holds two very bright glowing sticks. When the angle changes to a ground level view of Lois's legs, the man disappears.
Continuity mistake: On the Golden Gate, the school bus smashes a blue beetle car, a second later the car appears in perfect condition.
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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