Continuity mistake: The cheerleading equipment is knocked down from the bench, but magically appears up on the next shot.
Continuity mistake: The Hoover Dam breaks in many pieces with huge cracks everywhere. When Jimmy is hanging about to fall, from his POV there are just four tiny cracks.
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.
Visible crew/equipment: During the first scene in the Daily Planet, after Lois exits Perry's office saying "You forgot my report", two big stage lights get reflected on the left glass door.
Revealing mistake: After saving Jimmy from falling to the dam, during the flying sequence a couple of wires are seen between them.
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".
Plot hole: When Superman goes after the missile that's heading for New Jersey he leaves Metropolis (which is actually New York City). He would have met the missile head on, but he appears to catch up to the missile from behind and while it's still over territory somewhere around the Grand Canyon, so he probably could have stopped both missiles before the second one hit the fault line.
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.
Revealing mistake: In the extended version, when Luthor fires snow at Superman, the icicles bounce, rather than shatter, revealing they are some type of foam or plastic balls.
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 the burglar falls from the building, his flashlight is sometimes swinging, but other times it's flat against his body revealing the camera was tilted.
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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