Continuity mistake: When the Kent's stop the truck and see the cradle, the sky swaps from sunny and clear to heavily cloudy in a second.
Continuity mistake: When Kent's father pulls over his car, he holds the steering wheel with his right hand on the top. From the side, barely a frame before, he has his left hand on the side.
Continuity mistake: The way the bags are positioned in the Kent's pickup differs between the side and back angles.
Continuity mistake: In Lex Luthor's lair, the bottles to the left of the TV broadcasting the news disappear in the following shot.
Continuity mistake: When hanging from the bridge, the damage on the school bus' hood is different depending on the shot.
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.
Revealing mistake: On the Golden Gate bridge, the beetle car that skidded a split second before appears totally empty when the van crashes against it.
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).
Deliberate mistake: Before Superman traps the black missile, its beam is really big and covers half of the lettering on the side. When Superman is behind, the fire is much smaller and the lettering is visible, allowing us to see Superman.
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.
Other mistake: On Perry's office, there's a painted sign on the glass that says "Editors Secretary". Being the Daily Planet such an important paper, and with Perry White so picky on grammar mistakes, someone should've noticed that an apostrophe is missing.
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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