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.
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.
Continuity mistake: 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.
Continuity mistake: On the Golden Gate, the blue beetle skids and stops with the rear tyres on top of a painted white line. A frame later the car is on the middle on the white line.
Continuity mistake: When Otis is reading the paper about the meteorite found in Addis Ababa, the amount of chocolate in the candy bar increases or decreases depending on the shot.
Continuity mistake: The lights on the heliport keep swapping from facing the ground to pointing at the sky between shots.
Continuity mistake: The telephone poles close to the gap on the railroad disappear in the wide angles.
Continuity mistake: Inside the cab arriving at the Daily Planet, the fruit stall has no van behind. Immediately afterwards, a van appears.
Continuity mistake: Liz places her kitty on her right shoulder and on the next shot the cat's gone.
Continuity mistake: In the extended version, when Superman talks with his father in the Fortress of Solitude about being a hero, one shot shows the crystals reaching up to Superman's waist. In the next shot they are at ankle level.
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.
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)
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.
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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