Continuity mistake: When the cops are frisking J, the small cop on the left's left hand keeps changing position in every shot, with no logic whatsoever. (00:41:00)
Continuity mistake: When K sees the dead Chinese manager pinned to the wall, the manager's facial expression and position of his head changes between shots in a mere half second. (00:15:45)
Continuity mistake: When K tells J he's suspended, J moves his right hand away, yet when the angle changes it's back in its original position and he's moving it away again. (00:19:35)
Continuity mistake: When the 60's cops stop J by the billboard sign, he pulls over by the left end of the sign. In the close-up, the car is parked right by the middle of it. (00:40:20)
Audio problem: When the alien cuts Boris's shackles they hit the floor and make a metallic sound, yet when the chest armour falls it sounds like the foam object it really is made of. (00:03:40)
Continuity mistake: When the Afro-American military man lays dead, his cap changes positions between shots. (01:33:10)
Continuity mistake: When J chases Boris in 1960s New York he exits The Factory and runs on the sidewalk past a black car and a lamppost. A frame later, the car is gone and he's running on the pavement, on the space left, to allow him to step on the green car. (01:01:30)
Continuity mistake: When J is being swallowed by the fish, the floor around him swaps from very dirty, to slightly dirty, to spotless between shots. (00:16:15)
Continuity mistake: At the 1960s HQs, K places his hand on a notebook. A shot later it has jumped next to a typewriter. (00:44:40)
Other mistake: J exits the Flatiron building and a woman in a yellow dress starts walking behind him. He looks at the street ahead and the same woman is walking from right to left. (00:38:35)
Continuity mistake: When the cop is about to dip his finger in the cake, its position and distance to the cake keeps changing in every single shot, with no logic whatsoever. (00:03:00)
Continuity mistake: When J is in the car with young K, about to head for the bowling alley, the way J holds the matchbox changes between shots. (00:49:55)
Factual error: In 1969 while Boris is riding his motorcycle on the boardwalk in Coney Island, he rides in front of Nathan's Famous. In 1969 the only Nathan's Famous was on Surf Avenue. It wasn't until approximately 35 years later, in the mid 2000s, that Nathan's opened a smaller satellite store physically on the boardwalk. (00:39:30)
Continuity mistake: When Boris shoots spikes at the door that K and J are holding, one of them gets stabbed on the upper part of the glass. When the angle changes it's stuck on the center part. (00:17:40)
Continuity mistake: At the Chinese restaurant, when K and J are eating, J's white napkin keeps moving around between shots, as do some of the saucers and cups on the table. (00:13:45)
Continuity mistake: When J drags Warhol backstage, the people they pass-by have no continuity between the front and back shots. Note the tall transvestite with bulky hair they bump into first, who, a shot later, appears several meters ahead. (00:55:45)
Factual error: The ArcNet deploys after the Apollo 11 jettisons its launch escape system tower. This is the white tower at the top of the Saturn V stack attached to the white launch escape cone that covers the command module capsule that houses the crew. The idea is that if there is an emergency the LES will leave the crew capsule from the rest of the rocket and ferry it away so it can deploy parachutes and land during an abort. The tower connects to the cone through metal trellises. At some point during the launch when an LES abort is no longer an option, the ship will jettison the LES tower, which fires its rockets to pull the cone away from the capsule. As shown in MIB3, the tower with the ArcNet detaches at the trellises, leaving the white cone in place with no way to detach from the command module. The launch also shows spent debris falling over the middle of North America when it would be falling over the Atlantic Ocean. (01:32:30)
Continuity mistake: As soon as Boris blasts the door down, there are guards on the grounds and guards behind some of the cells in the background. After Boris blasts the the steel wall, the guards on the grounds are sucked into the vacuum of space, but the guards hiding in the cells in the background have vanished completely. They certainly weren't sucked into the vacuum of space because they were protected by both the cell bars and the ceiling above them. (00:04:50)
Factual error: When J walks through Coney Island's Luna Park in 1969, the Tickler roller coaster can be seen in the background. However, it is a spinning Wild Mouse coaster, which wasn't introduced until 1997. (00:41:55)
Continuity mistake: As O is helping K into the jet pack harness, he asks her if that is right. She says "Unfortunately it is." In that shot, she is looking up at him right into his eyes. It cuts to a side angle and she is suddenly looking at his mouth and chin. (01:19:15)
Chosen answer: The gold saucer crashed in middle of the street was the ship Boris stole to get to earth. While they are in the restaurant Kay gets a call that tells him a ship was taken from lunar max and it was Boris who took it.