Continuity mistake: When the train is about to derail, we see a bunch of goats and donkeys under the bridge, with a kid dressed in jeans and a blue shirt, and a bearded man with a white jacket. When the shot changes, the man is wearing the kids' clothes and the boy has vanished.
Continuity mistake: Lois leaves the gas station but the reflection of the glass shows it still there.
Continuity mistake: At the heliport, a cork bulletin board on the wall appears and disappears between shots.
Continuity mistake: When Lois is about to ride on the helicopter, there's a man in the background easy noticeable because he holds two very bright glowing sticks. When the angle changes to a ground level view of Lois's legs, the man disappears.
Continuity mistake: On the Golden Gate, the school bus smashes a blue beetle car, a second later the car appears in perfect condition.
Continuity mistake: When the helicopter is spinning around two men run towards the control room. In the next angle they're gone, only to appear entering several seconds later.
Continuity mistake: The huge lamp post next to the bus on the Golden gate disappears when the bus is about to fall down.
Continuity mistake: At the end of the falling Hollywood sign, the girls are zooming away from the sign. Angle cuts brusquely and, though the sign keeps falling on top of them, the girls are now walking calmly forming a neat cue.
Continuity mistake: When the gas station collapses, at first the roof falls down completely and covers the gas tanks, but in the next shot it's slightly laying sideways.
Continuity mistake: When Hoover Dam is about to explode, there's a shot of a resort nearby. The people running close to the fallen umbrella differ between shots.
Continuity mistake: Superman lands on the sidewalk looking for Luthor and a group of people gather closely together behind him. In the next shot, half a second later, they are standing way apart from each other.
Other mistake: In the extended version, there is a scene where the people are watching the news about Superman saving the chopper. The TV shows footage from below and from the other side of the building - no one could take that shot.
Other mistake: At the time when Lois is on the train and sees Clark running alongside, she is about 8-10 years old. About 12 years later she is 30.
Continuity mistake: The blanket used by baby Kal El to get to earth is red, blue and gold. When he lands it's just red.
Continuity mistake: When Superman pulls Lois' car out of the quake hole, the camera then does some wide shots, rotating around the scene before Superman flies off. The damage to the front of the car changes in these shots.
Revealing mistake: When in the prison yard, Luthor's bald cap is hanging loose around his nape.
Revealing mistake: When Lois falls from the helicopter, the cable holding her is visible.
Continuity mistake: After the van crashes against the beetle car, the new angle shows the van in a different position.
Other mistake: When Superman helps the airplane his "S" is flipped.
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.
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.
jshy7979