Continuity mistake: While Lex is telling Superman his plans with the missiles at his home, he is touching his cane with both hands then only then both hands back again.
Continuity mistake: While Lois and Superman are being mugged in the alley, Lois kicks the thief and protects herself leaning with her face against the wall and her arms widely spread. A frame later, when Clark grabs the bullet, her arms are close to her head.
Continuity mistake: In the extended version, in the scene where Martha is preparing breakfast, in the interior shot, she places a box of Cheerios on the table. Then she looks out the window at Clark. The shot changes to an exterior shot of her looking out the window, but the angle of the box of Cheerios has changed. (00:38:35)
Continuity mistake: In the extended edition, before Superman enters Lex's lair his hair is short, then when he's being shot at, his hair is much longer and bulkier. When he finally enters the place, it's back to short.
Continuity mistake: The two cops are following Otis at Grand Central Station and two girls, one in yellow, pass by their left side. When the angle changes to a closer one, the girls are in the back and pass by again.
Continuity mistake: Lois exits Perry's office and Clark enters to talk about salary. His hat swaps from facing up to down between shots.
Continuity mistake: When Clark is about to jump in front of the train, there's a crossing sign shaped as an X. Depending on the shot the front upper left part is either bent and about to break, straight, or missing.
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.
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.
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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