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. (01:02:05)
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Suggested correction: The building is in lockdown so it is no surprise that the lift is changed to a less flamboyant version. Even in the first scene, there are some doors there.
Continuity mistake: When they land on the roof of the launch site, Jay gets out of the passenger side, even though he and Kay switched spots after which Jay was driving/flying.
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