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: 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: 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 Jay. (This is mentioned in the DVD Audio Comentary with Barry Sonnefeld.)