Continuity mistake: The first day in the Daily planet, Lois starts typing and a man is sitting beside her. In the following angle the guy is standing several meters in front of her.
Continuity mistake: When Clark first meets Lois and the staff of the Daily Planet, he is wearing a handkerchief in his suit pocket. After using it to wipe up the spill from the soda, he stuffs it loosely back into the pocket when he exits Mr. White's office. A couple of shots later, it is neatly folded back into a triangle. (00:53:15 - 00:54:15)
Continuity mistake: At the police station, the counter swaps from being stacked with papers to semi empty when the angle changes.
Continuity mistake: When Jimmy is rescued by Clark in the Hoover Dam, Jimmy's hair during the flight is way longer than when he was hanging.
Continuity mistake: During the first scene inside Perry's office there's a radio on the background resting on a white book and a fat red volume. The white book changes positions depending on the angle.
Continuity mistake: When Lois's car first runs out of gas, the car radio is running. When Superman comes back after turning back time, the radio is off.
Continuity mistake: When the young soldier is about to reanimate Ms. Teschmaker his helmet is behind her arm. When the Captain lifts him up the helmet appears one meter away from the arm.
Continuity mistake: Jor-El teaches about Einstein during Kal-El's voyage to Earth, but when Superman talks with him in the Fortress, Jor-El says "I will have been dead for many thousands of YOUR years".
Continuity mistake: Superman's hands' position when holding the fuselage of the plane swap between shots.
Continuity mistake: When young Clark is running next to a train, he passes by a pole on the ground. Half a second later the angle changes and he is inches away from the pole, which he passes by again.
Continuity mistake: When Superman and Lois are being mugged in the alley, watch Clark's tie before and after entering; there's a thick blue coloured stripe near the knot, which later disappears.
Continuity mistake: When Krypton is exploding, Superman's mother looses her balance and falls backwards. In a new angle a frame later she is up-straight loosing balance again.
Continuity mistake: The first shot of Lois' red car shows it clean and shiny, a second later it's all dusty and dirty.
Continuity mistake: When Luthor smashes the green car, its wreckage is different in the shot when the soldiers arrive: The hood is open wider and the windows are broken.
Continuity mistake: During the trial, Zod and Ursa swap places in a couple of brief shots.
Continuity mistake: At the end of the football game, a guy with a cap tells Clark to have the clothes ready. But his lips are not in synch.
Continuity mistake: When Clark Kent falls out of the window of the Daily Planet and turns into Superman you can see that he is still wearing slacks and not blue tights.
Continuity mistake: By the cradle, Jor-El and her wife are standing a couple meters apart. In the next shot they appear closer together.
Continuity mistake: While being mugged in the alley, Clark's gabardine keeps swapping between neatly folded to wrinkled between shots.
Continuity mistake: When Lex Luthor calls Superman and the dogs bark, a group of trash cans disappear from the right of the black and white dog.
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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