Continuity mistake: The close shot of the dogs and the garbage bins shows stuff on top of the bins. In the next angle they're gone.
Continuity mistake: When Lois is hanging from the helicopter, she looks down and sees some cars on the pavement, by the entrance of the Daily Planet. From a ground view the cars are gone.
Continuity mistake: The morning Clark leaves the home farm, the sky keeps changing throughout the sequence: Dawning, clouds, sunny, dawn again, cloudy, back to sunny.
Continuity mistake: Superman saves Air Force One lifting the wing with his right hand and then salutes with his right-hand, suddenly holding the wing with his left.
Continuity mistake: When young Clark is left cleaning the football equipment, the students' car drives away, passing by a blue pick-up. The engine noise fades away and silence falls. When the shot changes, the car is suddenly meters behind, next to the blue pick-up, engine roaring again, and leaving the place again.
Continuity mistake: Mr. White dismisses the surrounding people while holding a cigar in his hand. From the opposite angle it's in his mouth. (01:20:26)
Continuity mistake: Superman arrives at Lois' place, arms crossed. Then uncrosses them and lowers his left arm. From the opposite angle it's bent.
Continuity mistake: When Teschmacher climbs the bridge she is barefoot, but when she arrives to the truck she is wearing high heels which were nowhere to be seen in her utility belt.
Continuity mistake: When Superman arrives at Lois' place she says "Don't fly away" and her hands are against her chest. A shot later her arms are extended.
Continuity mistake: When Johnathan Kent has a heart attack he passes by a harvest machine, walks several meters and collapses next to the house. In the close-up where he grabs his arm he's moved several meters behind and is next to the machine.
Continuity mistake: When Ms. Teschmacher saves Superman from drowning he is face up, but a shot later he is face down and swimming.
Continuity mistake: After Clark jumps over the railroad track there's a close-up of the train speeding by and it's obviously empty, no sign of the people that were previously seating inside.
Continuity mistake: In prison while Otis repeats what Luthor says he has a cop's hand on his shoulder or not, depending on the shot.
Continuity mistake: When Superman arrives at the broken railroad track the gap is huge, but when he places his body in between the tracks it is exactly Superman's height.
Continuity mistake: When baby Clark lifts up the truck, Martha's grip on his husband changes: In the close-up she grabs his chest, but in the wide angle she grabs his ribcage. This changes back and forth several times.
Continuity mistake: While Lex and Otis are talking with the lieutenant and his crew at the bridge, the sun changes between shots.
Continuity mistake: In the extended version, where Martha is preparing breakfast, she places a box of Cheerios on the table. Then she looks out the window at Clark. The shot changes to an exterior shot of her looking out the window, but there is a pitcher of milk next to the box of Cheerios that was not there before.
Continuity mistake: While Lex is telling Superman his plans with the missiles at his home, he is touching his cane with both hands then only then both hands back again.
Continuity mistake: While Lois and Superman are being mugged in the alley, Lois kicks the thief and protects herself leaning with her face against the wall and her arms widely spread. A frame later, when Clark grabs the bullet, her arms are close to her head.
Continuity mistake: In the extended version, in the scene where Martha is preparing breakfast, in the interior shot, she places a box of Cheerios on the table. Then she looks out the window at Clark. The shot changes to an exterior shot of her looking out the window, but the angle of the box of Cheerios has changed. (00:38:35)
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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