Continuity mistake: When Frank the dog is growling at the agent in the park his teeth are fine but later talking to Zed he is told he can have better dental. He smiles and his teeth are horrible. (00:23:50 - 00:31:10)
Continuity mistake: In the scene at the lockers in Grand Central Station, Agent Kay takes his watch, an illuminated Hamilton digital, back from the little animals living there. In one shot, Agent Jay puts an analogue watch in the locker as a replacement, but in the next shot it is the same old Hamilton digital owned by Agent K. (This is mentioned in the DVD Audio Commentary with Barry Sonnenfeld). (00:51:15)
Continuity mistake: When Agents Jay and Kay are in the elevator avoiding the garbage can robot who is shooting at them, watch their hands - they move from the wall to the roof ledge for support as the camera angle changes. (01:02:10)
Continuity mistake: When Jay is trying to tranquilize Jeff he gets hit in the head by a crossbeam which lays him back on Jeff's back. You can see that the syringe is not in his hands or his mouth, but when he sits back up he has it in his mouth again. (00:08:25)
Continuity mistake: At the beginning of the movie, when Serleena first lands on Earth, her ship crashes into the ground and creates a mound of dirt. When Harvey the dog comes over to check it out, the mound is gone. (00:04:43)
Continuity mistake: When Jay is giving Kay his favorite gun "little cricket" he is seen holding it by the lower part of the handle. The camera angle changes and he's holding it differently. The camera angle changes again and he back to holding it by the lower part of the handle. (00:31:45)
Continuity mistake: When Agent Jay and Tee are talking in the diner, a young guy passes behind Jay towards Tee, but disappears when the angle changes. (00:13:10)
Continuity mistake: When Lara Flynn Boyle is holding up Tommy Lee Jones with her tentacles, in one shot you can see the tentacles coming out of her fingers, but when they show her up close, there are no tentacles coming out of her fingers. (01:04:15 - 01:06:45)
Continuity mistake: After Jay and Kay go to see Jeebs about the deneuralizer, Kay leaves and the bad aliens come crashing through the walls. Jay shoots Jeebs head off and, as it's growing back, he says he got shot "right in the pie-hole" (mouth). However he was facing away from Jay when he was shot and it was above the mouth area. (00:40:25)
Continuity mistake: In the scene where Jay is fighting with Jarra, we see the clear rubber tubes in very back of the room. After defeating all the Jarras there is only six seconds left to stop the launch. He could not make it from the back of the room to the rocket in time to stop the launch. (01:05:10)
Continuity mistake: When J and Kevin get flushed they end up in 2 cans in times square. In the long shots the cans are the same height, but in close ups, Kevin's is slightly shorter than J's. (00:35:30)
Continuity mistake: When J is trapped by the subway slime monster there are no cars on the left and a big mess is done on the curb and pavement. However, from the opposite side of the street, a frame later, the place is full of cars with no sign of the previous destruction.
Continuity mistake: When Kay shoots Jeebs' head off, him and Jay are shoulder to shoulder looking down at Kay. Jeebs' head acts like a popped balloon full of green goo, but none of it gets on Jay or his suit. (00:41:20)
Continuity mistake: When Jay is in the fight scene with Jarra and his clones, Jay jumps up two clones to get to Big Jarra, but when the camera angle changes, the Jarra clone he jumped on is gone. (01:04:35)
Continuity mistake: During the fight scene with Jarra, Jay is dropped into the center of some large plastic tubing, but when the camera cuts to a closer shot, Jay is now seen at the edge of the plastic tubing. (01:05:15)
Continuity mistake: In the scene where Serleena confronts Zed in his office, look closely at her hands. Immediately after releasing Zed from her tentacles, her left hand now holds a box of Burger King fries, which disappear from shot to shot. This is most evident when she picks up the cellular phone, placing both empty hands on the desk first. (00:45:35)
Continuity mistake: In the scene where Agent Jay is looking at MIB HQ and sees the dead alien with tentacles, he sees something (Frank). He tells the computer to zoom in and when it does the tentacle on the right hand side half way up the screen changes shape and position. (00:36:40)
Continuity mistake: When Jay and Tee are at the diner eating pie, when Tee starts to eat his pie a woman with a purple shirt and black skirt walks by. When Tee Starts to cry, a few seconds later, there is a shot of Jay and the same lady walks by again. (00:12:45)
Continuity mistake: When Jay and Kay make their visit to Jeebs, Jay is talking to Jeebs and you see Jeebs making a statement about how his business is 'banging' and when he see Kay walk in, he points both his hands at him. The camera angle changes and Jeebes is now seen with only one hand pointing at Kay. (00:36:15)
Continuity mistake: When Kay and Jay are watching the movie about the light, Kay starts to remember the real story and cries. The shot later, his is cheek is dry. (00:56:55)
Chosen answer: It's referring to the innate racial prejudice some people have - an inflatable black guy driving a nice car got pulled over, whereas an inflatable white guy had no problems.