Continuity mistake: When hanging from the bridge, the damage on the school bus' hood is different 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: When Ms. Teschmaker is sunbathing, the trolley by her side is close to her thigh. In the wider angle is by her ankle.
Continuity mistake: When Jimmy runs towards Hoover Dam his hair is long. A fraction of a second later it's very short.
Continuity mistake: After Jor-el talks to Von-Dah he places his hands on a man's chest. In the following shot they're on his shoulders.
Continuity mistake: Before the school bus crashes, a brown car is seen coming. When the angle changes we still see a brown car but it's a totally different model.
Continuity mistake: In the gas station, the "closed" sign falls down but appears up in the next shot (you'll find it in the right side of the screen).
Continuity mistake: Perry White shows newspapers with day shots of Superman, but he made his appearance at night.
Continuity mistake: When Lois dies, Superman's face is covered in dirt. When he takes off and flies, it's clean.
Continuity mistake: When the gas station falls down, watch the right side: A green car with an open hood suddenly gets replaced by a red car.
Continuity mistake: When the school bus smashes the Golden Gate fence, the aerial shot from the back shows the fence complete, the shot from the front shows it smashed.
Continuity mistake: When Lois dies, the first time Superman sees her the left side of her face has sand and rocks around her cheek. When the angle changes they are at shoulder level.
Continuity mistake: When Superman avoids the train from derailing, the wide shot shows his cape fluttering but the close one not.
Continuity mistake: When Superman moves the school bus away from the void, the wide shot shows a different fence and wreckage, with a long piece of fence missing. The close shot shows a missing space that is slightly bigger than the bus.
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 Superman saves the wrecked plane, from the outside shots the window has droplets of water, but from the copilot's POV the glass is clean.
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.
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.
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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