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.
Revealing mistake: When Superman and Lois begin their flight from her apartment, a pair of wires suspending each of them are visible, especially on the Blu-ray.
Revealing mistake: All the footage of the missiles being launched is of a poor quality and grainy, which is inconsistent with the good quality of the rest of the shots, revealing that it's stock footage.
Revealing mistake: Superman has just saved Jimmy at the dam and is holding him in the air. Jimmy's fringe is standing up thanks to some hair fixer to achieve the effect of wind blowing (though it's a green screen effect). When Superman sets him on the floor his hair remains up giving away the trick, until the angle changes and it looks all combed and nice.
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.
Revealing mistake: When Superman takes Otis and Luthor to the prison wires holding them are visible.
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.
Revealing mistake: When Superman leaves the prison, wires holding him are visible.
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.
Revealing mistake: When Superman lands the burglar, wires holding him are visible for a brief moment.
Revealing mistake: Under Grand Central, the train that passes by Otis is the same one (5048) that kills the cop.
Revealing mistake: In Grand Central Station, the same extras appear in every scene, no matter where in time or place occurs.
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.
Revealing mistake: After Superman saves the cat, he takes off and wires holding him are visible.
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.
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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