Deliberate mistake: When MIB agents exit the lift to get into the main hall of the MIB Office, the lift opens halfway up the wall and they need to go down a little platform. But when K and J return during the lockdown and face the trashcan with guns, the lift opens at floor level, so it can be conveniently peppered with bullets.
Visible crew/equipment: When Agent Kay is in the elevator with the little worm dudes he swings down and starts shooting at the robot. When he swings down you can see the safety harness between his legs.
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.
Visible crew/equipment: When Jay enters the tent in which the small alien craft had landed we can clearly see the camera man in the golden reflection. This happens twice.
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).
Continuity mistake: When Agent Jay is in the yellow tent with Serleena's tiny ship, he pulls out his video communicator and begins to talk to Zed. Zed can see Agent Jay via the communicator but when Jay closes the communicator and puts it away, Zed still has a view of Jay speaking with him over the big, egg shaped monitor. How could Zed see Agent Jay over the monitor if there was no video device available to transmit the conversation?
Deliberate mistake: When the trashcan opens fire on the lift with Jay & Kay in, the distance and angles mean it would, at most, be able to hit up to the edges of the rear doors. When the inside of the lift is shown, the bullets have somehow managed to reach right to the edges of the lift.
Continuity mistake: When Jay and Tee first start to talk to Jeff, Tee grabs the "weed." When Jeff gets mad and starts banging on the grate, the wide shot shows Tee in the same position, gripping Jeff's weed, however it was not digitally added in that shot, so he's gripping nothing. But in the next shot, he's shown gripping the weed again.
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.
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.
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.
Deliberate mistake: The opening of the film says it takes place in July 2002, but when we first see Will Smith you can see the World Trade Center in the background which had been destroyed ten months before. [The film was made before the 9/11 attacks, and the towers were left in as a sign of respect - still a mistake, but there's the reason.]