Continuity mistake: In the jewelry store, when J chases the farmer, the boots behind him swap from standing to fallen between frames. (01:03:35)
Continuity mistake: When J exits the jewelry, he falls on a some trash with a pizza box next to his armpit. A frame later, the box is laying by his hip. (01:03:45)
Revealing mistake: In the scene after J shoots the exterminator van off of the tow truck he shoots again. When the camera clips to the tow truck driving away, you can see the smoke generators emitting smoke from the curb. (01:03:50)
Visible crew/equipment: When Tommy Lee Jones shakes the dog asking him about the galaxy, right before they exit the car, you can see the cameraman's reflection in the shiny black door frame. (01:06:30)
Other mistake: Soon after Jay pushes the little red button on the Ford POS, Kay inserts an eight track cassette. If you look at the eight track player, you can read "Select". The car is upside down at this point, but the word "Select" on the player, as well as the title of the cassette, "Elvis 'Promised Land'" are both right-side up. This means that, if the car were right-side up, the text would be upside down, and, in turn, the entire cassette player would be upside down. It is clear that this mistake was made by not paying attention to the orientation of the car as the scene was shot. It is also clear that the shot is done with the camera right-side up since Kay is in the driver's seat, which, right-side up, would be on the left, but since the car is upside down, he's on the right, which is seen when he inserts the tape. (01:14:20)
Continuity mistake: When J is searching for the cab, K arrives to pick him up and says "He won't be leaving in a cab". Right then a bus suddenly appears on the right lane, only to disappear in the next angle. (01:14:40)
Continuity mistake: When the countdown timer for the destruction of Earth appears on the viewscreen, you see it count down to 59:56. There is a cut to three cast members including Will Smith and Tommy Lee Jones for a brief dialogue scene. When it cuts to Will Smith walking away you can see the clock still counting down on the screen in the background. Now it is showing the time of 59:54. The aforementioned dialogue section took noticeably longer than two seconds. (01:15:45)
Audio problem: When Will Smith is looking at the two space ships at the MIB headquarters, if you look in the background Zed and K are there typing on the computer. But if you look closer you can tell that they're not even touching the keyboard and the sounds are just added into the movie. (01:16:00)
Revealing mistake: When J and K are knocked over by the roach near the end, when they land you can see a square of grass move. Shows that a crash mat is covered with a bit of grass to make the landing easier. (01:19:20)
Continuity mistake: When J and K are shooting their guns at the space ship toward the end, if you look carefully, you can see the spark that ignites their guns to have the fire come out of the barrel. (01:20:25)
Continuity mistake: When the UFO crashes against the ground, K's hair moves wildly in the front shot, but remains still in the angle shot from behind. (01:21:00)
Revealing mistake: When Will Smith throws a rock at the escaping Edgar alien, if you watch the rock after it hits the alien, it disappears after hitting the ground. (01:23:20)
Continuity mistake: Towards the end, when J is fending off the Edgar Bug with the flaming branch, Edgar's mandibles are outside his mouth. Cut to a shot of J and the mandibles are inside his mouth. (01:23:40)
Other mistake: In the final scene outside the MIB headquarters, Kay opens the neuralizer and we see it open, but there is no sound. Later when Kay tells Jay that he hasn't been training a partner but a replacement, we hear the sound of the neuralizer opening and Kay tells Jay how to operate it. (01:27:45)
Continuity mistake: When J is changing in to his suit, he reaches in to the locker with his right hand and pulls out a hanger with a pair of trousers and a jacket on it. His forearm is bare and he isn't wearing a watch. Seconds later when he takes the shoes out of the locker with his left hand, his forearm is now covered by the long sleeve of a white shirt and he has a silver watch on. A few seconds later when he lays the jacket over the bench, both his forearms are bare and again he isn't wearing a watch.
Continuity mistake: After Will Smith holds the squid, the amount of slime on his jacket differs between the right and left shots.
Revealing mistake: When the alien takes off Edgar's skin, when he throws it to the top of the hole in the ground then drags it back, you can see its rubber skin. I read the correction too. And no. Human skin doesn't look like rubber glove material.
Factual error: When showing Orion's Belt on the screen the stars Alnitak and Mintaka are the wrong way round.
Other mistake: When K is searching for his wife on the computer, the zoom in highlight boxes don't match the videos.
Other mistake: When K is deleting all documents belonging to Edwards (later J), his passport says he was born in Indiana, but his birth certificate says he was born in Manhattan, New York.
Answer: The MIB - or K specifically - had already erased the memories of all the police that were involved to cover up the alien sighting. It stands to reason therefore that theyd already have a cover story in place - that is the report that the captain is reading, and for which he congratualtes J.
roboc