Continuity mistake: When the cat in on the table in the diner, the word "ORION" on the cat's collar is in normal capitalized block lettering. But when the cat is on the table in the morgue, the word "ORION" is in calligraphy. Also, the colour of the cat's collar seems to change between these two points. (00:42:40 - 01:08:15)
Continuity mistake: In the beginning, when K shoots Mikey, one of the cops gets covered with blue slime all over his face and hat. Watch the right side of the hat: The length of the slime differs between the front and back shots. It's more seen when the scene is about to end and the slime starts to fall down in the front shot, but stays still in the back one. (00:07:25)
Continuity mistake: When Will Smith and the other recruits are taking their written tests, the white table first appears to be situated between the second and third men from the left. When Smith goes to the table to pull it across the room, it is much further to the right of the scene. (00:24:25 - 00:26:35)
Other mistake: There is a mistake in the French subtitle translation. In the diner when the cook asks Edgar the Bug, "where's Ivan?" Edgar responds, "[I] gave him a break". The translator writing the subtitles must have thought he was saying "GIVE him a break" because the subtitle reads, "laisse-le tranquille" which means, "leave him alone". (00:42:10)
Continuity mistake: After Kay neuralizes Jay the first time, Jay 'wakes' up in a restaurant and Kay hands Jay a card. He tells him to report to that location. The address can be seen written on the back on the bottom edge of the card. Jay flips the card over to read the address and it's still on the bottom edge of the card. When flipped, the address should now be on the top edge of the card. (00:22:00)
Factual error: When showing Orion's Belt on the screen the stars Alnitak and Mintaka are the wrong way round.
Continuity mistake: When the Mexican alien is running away, the whole scene is all wrong: He runs for a long time and passes by many bushes and cacti, but when K takes out his gun, the alien is just 10 meters away. Plus, from the POV angle, he passes by the cactus to the left of the guard twice. (00:06:50)
Continuity mistake: The MIB applicants are all sitting in the testing room and Zed talks about how they are all the best of the best of the best like, "Rangers, Navy SEALs, NYPD". The only sailor sitting in the room is not a SEAL, he's EOD. You can tell because he is not wearing the Special Warfare badge on his uniform, he's wearing the badge for Explosive Ordnance Disposal. (00:24:35 - 00:27:30)