Continuity mistake: The way the word Otisburg is written on Lex's map changes between shots.
Continuity mistake: When Ms. Teschmaker is watching the Metropolis news, the glass by the TV swaps from being behind the sun-lotion cream to in front of it.
Continuity mistake: When Luthor takes the kryptonite out of the box, from a side view he holds it at waist level, from a front shot he holds it at chest level.
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.
Continuity mistake: In the wheat field, the clothes inside the cocoon change from being tucked inside a corner to visible.
Continuity mistake: By the craddle, Jor-El's hands are appart, a frame later they're holding the crystal.
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: When baby Clark is greeting the Kents inside the cocoon, Martha's hands change from resting on the sides to up.
Continuity mistake: In the footbal field, one of the megaphones that Clark kicks down appears on the bench in the following shot.
Revealing mistake: After jumping in front of the train, Clark runs leaving a white trace behind. Watch the grass on the lower right and you'll see the scene is speeded up.
Continuity mistake: The position of the baby when his mother holds him by the cradle differs in the wide and close shots.
Continuity mistake: When the truck falls on Jonathan Kent, the way Martha holds him changes between shots.
Continuity mistake: When the player takes Susie with him, a bucket appears from nowhere on the right side of the bench.
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: When the football game ends, Clark is holding a bundle of towels. A frame later, the towel is neatly folded.
Continuity mistake: Before Superman enters Luthor's lair, Teschmacher is laying on the couch and a bottle of Ambre Solaire is facing straight close to the TV. In the next shot the bottle is turned to the left.
Continuity mistake: After Lex Luthor opens the box with Kryptonite, Superman leans with both arms on a table. A second later he's leaning with just one arm.
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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