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)
Other mistake: At the very beginning, when K disintegrates the alien Mikey, an MIB cover-up team arrives on the scene and approaches K at a distance of about ten meters (roughly 30 feet) ; whereupon K instructs them: "Give me a splay burn around the perimeter with holes at forty, sixty and eighty meters from right here! Thank you!" The team members disperse a scant few steps and use their flamethrowers and extinguishers on the cacti and undergrowth in the immediate area for five seconds. However, the distances K describes (forty, sixty, and eighty meters) would require the team laboriously dispersing hundreds of feet into the desert. But five seconds later, they're still only about 30 feet away from K when he says, "That's good! Thank you!" (00:07:55)
Continuity mistake: After Laurel is abducted and Jay tries to find her in one of the cabs, Kay brings the LTD around to pick Jay up. The LTD stops beside Jay in a position parallel to the white lines in the road. Jay gets into the LTD and when Kay drives off the LTD has noticeably changed its angle to the white lines even before it begins to move.
Revealing mistake: When James Edwards (later, J) catches the alien in the beginning and has him next to a wall, the alien pulls out a "reverberating carbonizer with mutate capacity" to shoot J. A quick tussle, and the alien drops the gun. When the camera goes to a close up on the gun, watch carefully. You see it quickly fade out of view after it comes to rest, and replaced with a few burning sparkle effects to simulate disintegration.
Continuity mistake: When K and D are talking to Mikey, they are standing in a clearing with no grass on the ground. When Mikey spots the trooper behind him, he turns and starts running towards the trooper, and he is running down a pathway in the grass. When K shoots Mikey and he is blown apart, there is a shot from the trooper's point of view towards K and D, and the pathway that Mikey just ran down is no longer visible and K is no longer standing in a clearing.