Continuity mistake: When J is charging Boris and keeping track of the spikes that the alien shoots at him so he can dodge them on the second try, Boris first shoots and hits J in the left shoulder. Then the second shot hits J in the right as J says "right" and the third shot hits his left side. Then when he goes back in time a few seconds, the only thing to change is J knows the sequence of which Boris will shoot the spikes. Only it is different. J dodges the first one and says "right" as it passes his right side. Followed by two lefts, and then a forth one on the right. Yet previously, it was left first, then right, and then left again only three. It goes from left right left, to right left left right.
Continuity mistake: As the hand creature busts the shackles off Boris' legs in Lunar Max, you can see the bottoms of his pants over his metal prison boots. There are only a few folds and wrinkles over his left foot, and the pants over right foot are hardly wrinkled at all, or affected as the creature climbs up his right leg. But only a couple of seconds later, we see another shot of Boris' feet as the creature breaks off the metal sleeve of his arm, and suddenly his pants legs are very wrinkled. Boris was standing perfectly still the entire time. Boris' legs are also suddenly closer together.
Plot hole: Lunar-Max prison is obviously part of MiB, them creating it for the purpose of holding Boris the Animal, and other criminals of worth as well. A high tech prison built on the moon with cutting edge technology and armed guards out the boot. Boris trashes the place, sounding all kinds of alarms and busting out, even blowing a sizable hole in the side of one of the complexes. He then jacks a ship off the moon's surface and crashes it back down to Earth. MiB doesn't know about it until almost a full day later when they realise the ship they found was from the moon, and Boris had escaped. It makes no sense that it took them that long to find out the information. A maximum prison, especially one to contain aliens on the moon, would be in contact with MiB. And any alarm that goes off there, especially for a break out of a high danger prisoner such as Boris the Animal, would have sent an alert to MiB headquarters right off if there was any logic to their system at all. There is only about a 1.5 second delay for a message traveling at light speed to reach Earth from the moon due to its distance. So within seconds of Boris busting out, MiB should have already been mobilizing to track where he would be going and intercept. There's no way, that logically, Boris could have escaped, made it back to Earth, and been there for nigh a day without MiB knowing about it and having their agents already tracking him down.
Continuity mistake: After busting out of the cake and killing the two Lunar Max guards, Boris' hand creature goes to free him. It first blasts spikes at the shackles on his legs and busts them, then begins climbing up to work on Boris' arm piece. In the shot where his leg shackles come off, you see the spike the creature shoots at them stuck in the metal and hanging off to the side. But in the shot where his arm piece falls to the floor, these spikes have vanished from his leg shackles.
Factual error: When J goes to the electronic store to get the time jump piece from Jeffrey Price, all of the TVs in the store are showing "Wheel of Fortune", which in NYC is shown on ABC TV channel 7. But when the show is interrupted for the emergency story about the invasion, the TVs show NBC TV Breaking News, which is channel 4 in NYC.
Continuity mistake: When J is digging through files to try and find out what happened between Boris and K, O comes in and talks to him for a moment. As she is leaving, shots of J shows he is leaning back in his seat. But when O is shown, the glass wall she is by shows his reflection, leaning forward and slouching.
Continuity mistake: In the first Men in Black, when K is deleting J's history; He deletes his birthday which was in 1975. The third film is set in 1969 and when K meets a young J, he is about 7 or 8. This would mean he was born no later than 1962, not 1975.
Continuity mistake: When the racist cops are frisking J, one pulls out J's gun and questions him about it. In the reverse angles, the cop is holding the gun over J's shoulder with almost all the handle in his hand. In the shots showing J's face, the cop is holding the handle so that some of it is sticking down, and it is in front of J's shoulder.
Factual error: When J looks through the log book telling when Boris was sent back in time, one of the previous dates says April 31st. There are only 30 days in April.
Continuity mistake: As J pops his head up on the tall building, there are windows immediately behind on his right and left and both are closed. The camera pulls up and back to show the scale of the building, then cuts back down to J. Now suddenly the window on his right side is open, and the lamp in the room is on. The window also changes from closed to open a few times in this scene.
Factual error: In the film, in 1969, prior to the launch of Apollo 11 the moon is shown to be a full moon, however, in reality, on the night before the launch the moon was a tiny crescent moon.
Factual error: When J is travelling backwards in time, he passes the Great Depression and sees a couple of men jumping off the building. But nobody was ever recorded to have jumped off the Chrysler Building in the Depression. The only suicides committed were by gunshot.
Continuity mistake: When the huge alien fish throws J through the window of Wu's, J knocks over several rows of frogs hanging in the window as this happens. As he finishes being thrown out of the window, only one row of frogs is left. A few minutes later as K suspends J, K goes to exit Wu's and now there are suddenly two rows.
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.
Continuity mistake: When Boris' pet emerges from the cake, it kills the two guards. The Lunar-Max guard that had his hand stuffed in the cake has a spike put in his head and lands on the floor with his head resting against the cell wall. After the pet removes Boris' shackles, Boris goes to leave the cell and the guard with the cake on his hand is now lying on the floor almost entirely turned over.
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.
Factual error: When J arrives on top of the bird on the Chrysler Building in 1969, he looks around at the view. The North Tower of the World Trade Center (One WTC) should be in view. The construction of the North Tower began in the summer of 1968. In 1969, even though the very top was still under construction. The first tenant moved in. Even though One WTC wasn't officially finished until 1972, in July 1969, there should be a clear view of at least 3/4 of that tower.
Plot hole: At the ball park stadium, K, J, and Griffin are high up in the bleachers watching a future window of the Mets game. Boris suddenly drives by on a motorcycle up in the stands and grabs Griffin, then plows through the railing on the side of the stadium and falls down below, crushing K's car. He then speeds off instantly out of the parking lot with Griffin. Then suddenly, somehow, J and K are running out into the parking lot close to their car quickly enough to be watching Boris speed away from the parking lot on the road. There is absolutely no way K and J could have made it out of the stadium and out into the parking lot in just a couple of seconds like that.
Continuity mistake: As J is being put in the "big ass neuralyzer", they first have him in front of it strapped in a metal bracket. As they begin turning him upside down, the white suit guy on the right reaches over and begins opening the hatch on the neuralyzer. You see him turn the handle and hear the creak and see it slowly crack open for a moment before the shot cuts. Then two shots later as the white suit on the left is about to put the bite guard in J's mouth, the hatch is suddenly closed and the guy on the right is reaching over to open it again.
Continuity mistake: After K has placed the ArcNet on the Apollo rocket, he goes down a zip line and meets up with the Colonel on the beach. The shot from the zip line shows the colonel to be standing on the sand. Next shot, he's suddenly standing on the arrow signs between each zip line.
Continuity mistake: In the scene where J is being questioned by K, O walks up to to K, who picks up a cup of coffee and starts drinking it. The handle is directly in front of K on the opposite end of the cup in the first shot, but in the next shot, the handle is suddenly on the other side.
Continuity mistake: When Boris kills Roman the Fabulist, the spike he shot at his head is located to be just an inch or two above his eyebrows. When J finds the body a few moments later, the spike is suddenly much further up his head than it was a few moments ago. The spike has also shifted an inch to the left.
Continuity mistake: When the Lunar-Max guards take Boris' girlfriend to visit his cell, one of the guards opens the door. Just as the shot finishes, the cell door can be seen open enough for two people to stand side by side. From the other side, there's only enough room for one person.
Continuity mistake: When K tells J he's suspended after asking about Boris, they get into a brief confrontation about it. As K is storming away to take the car, leaving J back at Wu's without a ride, J's suit is still dirty, wet, and nasty from his fight with the alien fish. Moments later, J is seen going to MiB headquarters and now his suit is clean and in perfect order.
Deliberate mistake: The Army Colonel's Class A uniform does not have a name plate on the flap of the right breast pocket as per regulations. If the Colonel's name plate was present, there would be no twist to the movie.
Continuity mistake: In the scene where J and O are talking about the temporal rifts (just before they are alerted to the invasion of Earth) the ring on O's left hand keeps disappearing and reappearing.
Plot hole: When (future) Agent J and (future) Boris are fighting on top of the large red docking station for the spaceship, Agent J gets shot deliberately by Boris and jumps off the edge of the dock. Then he uses his time travel device to go back in time a few seconds earlier to be able to dodge the shots. There are a few mistakes in this part. 1) There should be another Agent J and Boris there too, as they have gone back in time to that moment again. However in the movie there are only two of them. 2) The injuries sustained by Agent J (the bone spikes in his abdomen) should have remained there when he went back in time. If it were true that you healed once you went back in time into the condition you were in at that moment, then Boris should have grown an arm back when he went back in time. 3) Due to the time loop, Agent J remembers how to dodge the shots, while Boris doesn't remember anything and is surprised by the outcome.
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.
Factual error: The flag of Spain shown at Cape Canaveral is not the official one used in 1969 but the one adopted in 1981.
Continuity mistake: At the diner, J says to the waitress K has apple pie. K is then given some apple pie. In one shot, the waitress is in the middle of giving K the plate with pie and the plate has not reached the table yet. But in the immediate shot afterwards, the pie has already reached the table.