Continuity mistake: After Superman saves the train from derailing, there's a wide shot of the lead locomotive and it has just one small window on the side. In the immediate close-up there's a big window where the conductor peeps, and a sudden second window with a handle bar where another engineer shows up.
Character mistake: In the Air Force One scene, when lightning destroys one of the plane's engines, one of the pilots tells a co-pilot to inform Metropolis Airport that the president is on board the plane. The crew is unnecessarily repeating themselves: just a few moments before, they radioed in that "Air Force One" was on approach; the plane would only have that call sign if the president was on board.
Continuity mistake: When the cab arrives in front of the Daily Planet, the sidewalk in front of the office is empty. A split second later there are people everywhere.
Continuity mistake: When Lois interviews Clark, the position of the glasses changes between shots.
Continuity mistake: When the cradle takes off, thousands of glasses fall on the floor, but the next travelling shot shows just four or five around the parents, and the rest of the floor clean.
Continuity mistake: When Superman arrives at the dam, after chunks of concrete have exploded everywhere seconds before, there is barely nothing broken, except for some cracks on the wall.
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: 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.
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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