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)
Deliberate mistake: When Alexander is travelling to the future for the first time, it shows a speedy acceleration of the events around him. However, the planes that are seen flying by are moving at normal speeds, or at least speeds way too slow since they should be moving too fast to even see, since skyscrapers are being built in a matter of seconds.
Deliberate mistake: When the woman is attempting to escape from the elevator, it dislodges and falls down, so then the actress is facing the ground...but when her arm hits the floor, the floor itself bends. If you watch the DVD with the commentary on, the director points out that it was a break away floor in case the actress' head accidentally snapped forward, to avoid any injury. (00:08:00)