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. (00:03:35)
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. (00:03:35)
Continuity mistake: After the time line is fixed, J meets K in the diner. In one shot, the spoon that is by K's plate moves to the edge of the table, then a few shots later it's back to its original position. (01:36:25)
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. (00:22:20)
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. (01:29:10)
Continuity mistake: When Boris asks the guards in Lunar Max to cut up the cake for him and his girlfriend, she turns towards the guards holding the cake. Her head is leaning slightly forward and tilted to the right. The camera cuts back some and suddenly her head is tilted left and back. (00:02:55)
Continuity mistake: In the first Men in Black, when K is deleting J's history; He deletes his birthday which was in 1969. 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 1969. (01:33:30)
Suggested correction: K First met J in 1969 and knows he will meet him again due to the time travel events in the movie. Agent O said that time travel was banned because it was so dangerous. Presumably, K could have been dismissed from the MIB if it was found that he knew of a time travel event and did not report it. Therefore, immediately following the events of the movie, Young K probably altered J's birth certificate himself, knowing that he could get away with it. Note the smirk on K's face in the first movie when he deleted J's birth certificate that he had altered himself.
In the first Men In Black, K very specifically says, "1968, well I guess you weren't born yet." to J.
Yes, because K still needs to cover up his involvement in time travel.
Continuity mistake: When K suspends J, the small cup on the counter keeps changing positions and moving further away between shots. (00:19:40)
Continuity mistake: When Griffin foresees the end of the baseball game his hands are on the J and K's backs, but a frame later he's grabbing their arms. (01:08:40)
Continuity mistake: When Boris says "You complete me", just after he is introduced near the start of the movie, the dead cop's head position changes. (00:04:00)
Continuity mistake: When J shows Jeffrey the alien invasion on TV, the notebook on the counter swaps from open to closed, and then back to open between shots. (00:32:25)
Continuity mistake: When Jeff sets the box with the time device in it on the counter, he begins to open it with one hand on the side of the box, and the other hand on the front of the box. It cuts to a close up and suddenly his hands are both on the sides of the box. (00:33:05)
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. (00:41:00)
Continuity mistake: When J and K are driving to Cosmic Lanes, they drive past the exact same white truck three times. (00:50:10)
Continuity mistake: When Jeffrey places the time-remote control on the counter it lays next to a notebook. In the close-up it's gone. (00:33:05)
Continuity mistake: At the electronic store, when J arrives, the headphones on the counter keep changing position between shots. (00:31:35)
Continuity mistake: After O delivers her eulogy for Z, J and K are in the car talking. The amount of cars and the style of the streets they pass-by have no continuity whatsoever between front and side angles. (00:09:40)
Continuity mistake: When K returns to the diner to leave the tip, he places down the money with his left hand and his finger is still on it as the shot ends. As it cuts to the next shot he is suddenly pulling his right hand away from the money. (01:37:40)
Continuity mistake: As J is telling K the truth about Boris killing him at the Moon Launch, one shot from behind K shows his head is down. The next shot, he is suddenly looking straight forward as he punches J in the face. (01:16:15)
Continuity mistake: When past and future Boris meet, past Boris turns towards future Boris completely and has his full body facing future Boris as he is walking toward him. But as future Boris is still walking towards past Boris and saying the line about spending the next 40 years in prison, past Boris suddenly has his body turned away from future Boris, and so future Boris has to step around in front of past Boris. (01:12:45)