Revealing mistake: When Jor-El is placing the baby Kal-El into the spacecraft, you can see his Rolex under his sleeve.
Visible crew/equipment: Just after young Clark Kent jumps in front of the train, there is a close up of the train speeding by with a very visible camera in its reflection. (00:30:00)
Continuity mistake: Kal-El's cradle arrives on earth, flies zooming past the Kents' car, which is driving in the opposite direction and crashes 500 meters behind the vehicle. The car keeps moving for about 200 meters and then pulls over. A brief shot shows an intact curb on the right. However, when Jonathan Kent gets out of the car, everything changes: The cradle has moved 700 meters ahead and lies next to the car; and the immaculate field is now destroyed by a huge ditch.
Visible crew/equipment: Near the beginning when Lois and Clark are walking out of the Daily Planet, Clark gets stuck in the revolving doors. But, look closely at the glass door, and you can see Richard Donner (confirmed in Superman expanded commentary) holding the door so that Christopher Reeve can get stuck.
Continuity mistake: Liz places her kitty on her right shoulder and on the next shot the cat's gone.
Revealing mistake: When Superman holds the plane's engine, the "S" on his shirt is looking the wrong way, revealing the angle was flipped.
Continuity mistake: When the three villains get trapped by the glass, Ursa's face and haircut are totally different.
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.
Revealing mistake: When in the prison yard, Luthor's bald cap is hanging loose around his nape.
Visible crew/equipment: During the first scene in the Daily Planet, after Lois exits Perry's office saying "You forgot my report", two big stage lights get reflected on the left glass door.
Continuity mistake: When the lady of Lex Luthor is in a red dress pretending to be unconscious on the road we see her legs flat on the ground, then in the next shot one leg is standing up.
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)
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: In the wheat field, the clothes inside the cocoon change from being tucked inside a corner to 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.
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.
Revealing mistake: Under Grand Central, the train that passes by Otis is the same one (5048) that kills the cop.
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: The way the word Otisburg is written on Lex's map 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.
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