Revealing mistake: Superman has just saved Jimmy at the dam and is holding him in the air. Jimmy's fringe is standing up thanks to some hair fixer to achieve the effect of wind blowing (though it's a green screen effect). When Superman sets him on the floor his hair remains up giving away the trick, until the angle changes and it looks all combed and nice.
Revealing mistake: When Superman takes Otis and Luthor to the prison wires holding them are visible.
Revealing mistake: When Superman leaves the prison, wires holding him are visible.
Revealing mistake: When Superman lands the burglar, wires holding him are visible for a brief moment.
Revealing mistake: Under Grand Central, the train that passes by Otis is the same one (5048) that kills the cop.
Revealing mistake: In Grand Central Station, the same extras appear in every scene, no matter where in time or place occurs.
Revealing mistake: After Superman saves the cat, he takes off and wires holding him are visible.
Revealing mistake: Before the Hoover Dam breaks, the places where all the cracks and water will later appear are easily traced on the concrete, covered in plaster and painted. Either that, or the real Hoover Dam has burst many many times and always through the same spots.
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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