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.
Other mistake: When Superman helps the airplane his "S" is flipped.
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 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.
Visible crew/equipment: While Lois chats with Clark and says "three kids, two cats" a microphone is reflected on a glass on the lower right corner. (01:03:50)
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.
Visible crew/equipment: When the cocoon cradle crashes and the Kents pull-over, lights and bulky object (camera?) are reflected on the driver's door, perfectly visible when he opens the door. Seconds later, rigs and filming equipment are visible on the fender.
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.
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