Other mistake: When Superman and Lois are flying through the clouds, there are a number of shots in which we see Superman from Lois' point of view. If you look closely, you can see that Christopher Reeve is not being suspended in these shots, but is, in fact, kneeling to look as though he is flying. You can tell by the profile of the red trunks.
Other mistake: When the camera pulls back from Superman in his Fortress of Solitude, right after the image of his father wanting to hug him disappears, you can see on the right of the screen that one of Superman's 'crystal' walls is fluttering or shaking like it's made of plastic.
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.
Other mistake: When Superman helps the airplane his "S" is flipped.
Other mistake: Clark does not have enough room beneath his clothes to have the suit, the cape and the boots.
Other mistake: On Perry's office, there's a painted sign on the glass that says "Editors Secretary". Being the Daily Planet such an important paper, and with Perry White so picky on grammar mistakes, someone should've noticed that an apostrophe is missing.
Other mistake: Something that happens a lot in films. When Lex Luthor is watching the cops trail Otis the image on Lex's CCTV screen is actually just the scene from the film being played back. The shots change to angles where Lex couldn't possibly have a camera, for instance a close up on the cop holding his partner's hat. This mistake is especially more noticeable in the extended edition where Superman walks through Lex's 'gauntlet'.
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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