Continuity mistake: When Superman lifts the plane during the storm, after the pilot asks what's going on, the copilot glances at the window grabbing its side. From the opposite angle he is away, repeating all movements.
Continuity mistake: When Clark shows Perry a white paper with directions of where to send the payroll, the way he holds the paper differs between shots.
Continuity mistake: The first wide shot of Superman arriving at the broken railway shows no logs hanging. The close shots, and then on, do show logs.
Continuity mistake: When Lois exits the alley where Clark grabs the bullet, her hair is much shorter than when she entered.
Continuity mistake: When Superman arrives at the ditch by the railway, the gap is 3 times his length. In the next shot the gap has shrunk and now measures exactly Superman's height.
Continuity mistake: When Superman is in Luthor's lair and Lex calls Ms. Teschmaker , the lamp on the floor changes from lit to unlit depending on the shot.
Continuity mistake: When Superman walks to Luthor's lair, the amount of snow on the bridge of the snow-chamber differs between the CCTV shot and the one from the inside.
Continuity mistake: After Superman breaks Luthor's door, on Lex's table a map is resting on a sculpture on the left. From a back shot, it isn't.
Continuity mistake: When Clark is shot by the mugger, his hat falls down. In the next shot, while Lois is screaming, you can see him taking his hat off.
Continuity mistake: When the council tells Jor-El not to worry them, a bald man standing in the back changes positions between shots.
Continuity mistake: The position of the baby when his mother holds him by the cradle differs in the wide and close shots.
Continuity mistake: After Clark runs by the train, a girl in a moving car stands up. In the next angle, a split second later, she is sitting down.
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.
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.
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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