Continuity mistake: When Henry has just shown De Niro the guns and he returns to his car, you see him light up a cigarette. When the shot changes the cigarette has vanished. (01:54:45)
Visible crew/equipment: When moving into their apartment Patrick Swazye kicks the statue to make it swing so they can get it inside. As they are looking at the statue, two moving men cross in back of them carring a mirror and as they pass you can see the director and camera crew in the reflection.
Visible crew/equipment: Watch for the boom when the cigar girl's Volvo boat swipes the building (it's on the top left of the screen on the widescreen version).
Deliberate mistake: Almost trivia, but not quite. When Mystique's looking through the guard files to find a suitable candidate, lots of photos flash up very quickly before she finds the guy she uses. Of note is that Bryan Singer pops up in guard uniform (with his own name), and so does someone called "Donner, L". This is most likely referring to Lauren Shuler Donner, one of the producers, and sex is specified as "F", but the photo is of a stubble-coated man. (00:23:10)
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)
Visible crew/equipment: Boom mic visible, reflected in Barb's motorbike helmet as she talks to Big Fatso.
Continuity mistake: Bruce Willis is emerging from an underground air-vent when the plane with General Esperanza is landing. Initially the plane is coming on a direct course for him and he struggles to get out. In fact the front wheel is on course with and knocks the vent cover. But in the very next scene, the tire marks clearly show the front wheel passed to the right of the vent and so completely missed it. (01:11:40)
Continuity mistake: During the scene where the police first go to arrest Howard and John is deciding which door is the right one his plastic face plate is down and in the next shot it is clearly up. (00:10:55)
Revealing mistake: When Nancy is running up the stairs in her house to escape Freddy for the first time her foot hits the steps and go through the steps into some goop. Look at the steps above that step and you can see the pre-cut holes where the next sets of goop will be. (00:39:10)
Revealing mistake: During the bedroom scene with Felicity and Fat Bastard you can clearly see the air hose that fills his suit when he rolls over in the bed. (00:49:10)