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 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: Just before the diner scene, where the two aliens are discussing the galaxy, we see the outside of the Russian restaurant. The neon sign says "haroshaya" meaning "good" all the way across the window, in the next shot inside the restaurant, the "ha", which looks like the English letters "xo", is gone and the sign is centered. (00:41:00)
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: When the truck gets smashed at the start, the tree beside the truck is well alight, but when the man comes out of the house, it is only a little alight. (00:12:40)
Revealing mistake: When Beatrice turns the sugar bowl over to dump the sugar into the glass, a barcode label and handwritten prop inventory number with the name 'Sony' can be seen on the bottom of the bowl. The film was made at Sony Pictures Studios. (00:15:15)
Continuity mistake: When the jeweller leaves his shop, the shop window clearly shows the reflection of the parked exterminator's van. Then you see the van being driven up the cross-street as the jeweller leaves in the taxi. Then Edgar/bug parks the van, goes to the shop, and you can see the same reflection in the jewellery shop window. (00:38:35)
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)
Visible crew/equipment: In the scene in the beginning where Will Smith chases the alien who jumps off the bridge onto the street. Will Smith jumps from the bridge onto a tour bus, then jumps on the back of a newspaper delivery van. In the passenger side of the van is a cameraman with his back towards the windshield in order to film down the side of the van as Will Smith jumps off the van. (00:10:20)
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)
Factual error: When Tommy Lee Jones is looking at his wife on the computer, he had typed in Truro (in Cape Cod, Mass.), but when he zoomed in, it was on the lower cape; Truro is located on the upper cape near the tip. (00:58:40)
Continuity mistake: After Will Smith holds the squid, the amount of slime on his jacket differs between the right and left shots.
Continuity mistake: In the restaurant scene, the jewel case containing the diamonds is to Mr. Rosenberg's right, but when the Arquillian asks what it is, the jewel case is to Mr. Rosenberg's left. (00:41:55)
Continuity mistake: When J and K first get in the car (the Ford POS),the windows keep switching from up to down. Interior shots Will Smith's window is up, exterior shots his window is down. (00:40:30)
Revealing mistake: There is a scene where Agent J is standing on a car and shoots the "Noisy Cricket" at the fleeing Edgar. The camera shot is from inside the car and just before Agent J crashes through the windshield, you see a precut area in the glass. (01:01:25)
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 J and K get into the car (a POS if memory serves) K makes a comment about J fastening his seatbelt, if you watch in the background out of J's window as they pull away there are a few people walking at an incredible rate showing that they filmed the scene at a normal speed then sped it up when put into the final cut. (00:40:40)
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: Throughout the whole movie it is summer. Green trees with leaves, green grass, etc. After the scene where Will Smith is deciding to become a Man in Black (summer), there is a shot of the Bug Mobile driven by Edgar where it is obviously winter. A wide shot of Manhattan with steam coming out of the tops of some of the buildings, and some trees without leaves in the background (winter). Then in the next scene and those following it is back to summer. (00:31:20)
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.
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.