Continuity mistake: As O is helping K into the jet pack harness, he asks her if that is right. She says "Unfortunately it is." In that shot, she is looking up at him right into his eyes. It cuts to a side angle and she is suddenly looking at his mouth and chin. (01:19:15)
Continuity mistake: As J is saying no jet packs, he has both arms out with his hands turned palm down. It cuts to a different angle saying there's a reason they don't have those in the future, and you can see his left hand. It is suddenly gesturing towards the machines but palm up. (01:18:40)
Continuity mistake: After being pulled over by the racist cops, J insults them and they pull him out to frisk him. As they have him bent over the car, one of them pulls out his gun and says "what's this, a concealed weapon". In the shot from behind J turns his head to the left to look at the gun. It cuts to a view of J's face as he says "Hey, it's his grandmother's suit." J is instantly looking straight forward. (00:41:05)
Continuity mistake: After the incident at Wu's restaurant, J walks up to a crowd of people and says "Can I have everyone's attention please?" As he does, he holds up his neutralizer. Just before the cut, you see him raising his other hand and points at the device. It cuts to show the crowd, then back to J. Suddenly he is repeating this exact same motion, the footage repeated as he points to the neutralizer. (00:18:20)
Continuity mistake: Before leaving in the jet packs to go to Cape Canaveral, O steps off K's jet pack twice between shots. (01:19:25)
Continuity mistake: When the little alien sneaks inside the Boris' hand, the fingers are stretched out in one shot, yet bent a frame later. (00:03:50)
Continuity mistake: The shot of Apollo 11 flying away from Earth shows spent fuel stages and other debris falling away. When the ArcNet deploys after a flash of light, all the debris disappears. The shield should envelop the debris as it falls back to Earth, not make it vanish. (01:32:30)
Continuity mistake: In the scene where J is being questioned by K, O walks up to to K, who picks up a cup of coffee and starts drinking it. The handle is directly in front of K on the opposite end of the cup in the first shot, but in the next shot, the handle is suddenly on the other side. (00:44:50)
Continuity mistake: As J is being put in the "big ass neuralyzer", they first have him in front of it strapped in a metal bracket. As they begin turning him upside down, the white suit guy on the right reaches over and begins opening the hatch on the neuralyzer. You see him turn the handle and hear the creak and see it slowly crack open for a moment before the shot cuts. Then two shots later as the white suit on the left is about to put the bite guard in J's mouth, the hatch is suddenly closed and the guy on the right is reaching over to open it again. (00:46:10)
Continuity mistake: At the Apollo rocket launch platform, J calls Boris the Animal twice, who lifts J up and launches him away. J glances at K, who's got both arms stretched out trying to save himself. A shot later, in the close-up, only his right arm is stretched out. (01:28:40)
Continuity mistake: When K mentions his grandfather, he turns his head away from J. In the next shot, his head is closer to J. (01:02:30)
Continuity mistake: When J is shown the time-jump gear, the box is to the left of a pair of earphones and just an inch away from the log journal in front. When the shot changes the earphones are between both.
Continuity mistake: When J is drinking his chocolate the glass is next to his mouth in the angled shot from in front, but lowered in the angle from behind.
Continuity mistake: When Obadiah stands on the Chrysler building terrace his hair is either loose or tucked behind his ear.
Continuity mistake: When K and J drive to the bowling alley, the same junction with a shiny blue car and a man wearing an orange shirt is seen three times through J's window.
Continuity mistake: At the bowling alley, after K polishes the alien's head, the way his hair is messed up changes between shots.
Continuity mistake: When K questions J at the headquarters, K grabs his tie. From the immediate angle his hand is lowered.
Continuity mistake: As J flies backwards after the fish creature sneezes, he breaks through the plate glass window, and has the bottles in his hands. After the cut, he's just breaking the glass, and the bottles are missing from his hands.
Continuity mistake: On the Apollo docking bay, just as J says "You're gonna lose", Boris has J pinned up against the scaffolding. Then as Boris says "Let's agree to disagree", J is suddenly not pinned against the scaffolding, leaning forward. J also goes from looking ahead to looking down. (01:28:35)
Continuity mistake: When Griffin shows J and K the vision of the baseball game, J walks back and then walks back over to Griffin. Griffin then places his arm around J and his hand ends up around the top of his arm. In the next shot, Griffin's hand is suddenly on J's shoulder. (01:07:05)
Answer: In MIB 3, if that's a preservation of the landing site, why is the top part on the lander? Surely it would just be the bottom part of the LIM, as the other part is used to leave the Moon?
This is not an answer to the question.