Continuity mistake: When they arrive at the ball park, K gives J his stuff back. The close up of the time device in J's right hand shows his thumb is closed in close to his hand. But the shot cuts to show both him and K, and suddenly his thumb is stretched out. K also puts his arms down twice during this part. (01:06:10)
Continuity mistake: At the diner, K asks J if he has a girl in the future. In that shot, J is looking down at his food. It cuts to a different angle and J is instantly looking straight forward as he is turning his head to K to say "I got you." (01:05:05)
Continuity mistake: At the diner, K says the "pie don't work unless you let it." J then looks at him and begins waving his fork at his own pie, but the shot cuts to a different angle and J is instantly looking down at his pie as he begins waving his fork. (01:03:50)
Continuity mistake: When Griffin is telling J that his buddy might give him antacids for his gastric distress, there is a small group of people behind him. One of them is wearing a picnic cloth style dress with red and white squares as the pattern. She walks away to the left of the screen, but then it cuts to a close up of Griffin as he says "But that depends" and she is suddenly right behind him. (00:58:50)
Continuity mistake: When J is in his lying fest at the 60's MiB headquarters, he starts calling two guys that walk past him "K." The first one walking by has a clipboard he is working on. He walks totally past J, and then another guy with nothing in his hands begins walking by and is almost passed J. Then the camera cuts to a close up of J, and the second guy passing him suddenly has stuff in his hand he is working on. (00:43:45)
Continuity mistake: As K is questioning J in the past at the MiB headquarters, there is a green alien behind J talking on the phone. In the close up of J as he's telling K to turn the power down on his tazer, and he can't feel his tongue, the MiB agent behind J is seen taking the phone from the alien and hanging it up. It cuts to K saying "How do you know my name?" then back to J in a shot further away. The green alien is seen handing the phone to the MiB agent again to be hung up. (00:43:35)
Continuity mistake: After the timeline is altered, J returns to MiB headquarters where he is met by Agent Double A in the elevator. After a brief monologue by Double A, J turns to him and says "Give me 5 feet, or I am gonna pluck you in your throat." He holds up his hand like he is going to flick Double A. In one shot, his wrist is bent up, but in the next shot, it's bent down. (00:26:20)
Continuity mistake: Jeffrey begins giving J a quick crash course on how to use the Time Jump device on top of the building. Just before he says "When you're moving fast enough" he pats J on the back, receiving an angry look from J. Jeff then puts his arms down as J begins slowly moving forward. The camera then cuts to a closer shot as he begins that line, and suddenly Jeff's arm is back on J's back, and J's arms are in a different position. (00:34:25)
Continuity mistake: Trying to crush the metal tray that J wedged in its mouth, the large alien fish breaks a tooth on the tray. J then picks up a couple of bottles of mustard and squirts its nostrils full. During that shot, the shape of the broken tooth has changed slightly, and the remaining piece is larger. (00:16:25)
Continuity mistake: Just before K says the line "I used to play a game with my dad..." at Wu's restaurant, he is looking straight forward. But as he begins saying that line, preceeding a sigh, the camera cuts to a different angle and suddenly he is looking to his right. (00:13:45)
Continuity mistake: When K slaps Wu with the Spikey Bulba the first time, you see Wu's head turn to the right as he's hit from the over the shoulder view. But when it cuts to show Wu's face, his head is suddenly being thrown back rather than turning right. (00:12:40)
Continuity mistake: As Boris says "I see you've brought me a treat, darling" to his girlfriend in Lunar Max, she turns her head from the guards and looks at the cake. It cuts to a closer view of Boris' face, and instantly she is looking at him instead of the cake. (00:02:50)
Continuity mistake: At the headquarters, when young K places the neuralyzer and gun on the table their position changes between shots. (00:44:00)
Continuity mistake: When young K starts questioning J, K's hands swap between crossed, loose, one on top of the other with no continuity whatsoever. (00:43:35)
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. (00:29:45)
Continuity mistake: In the lunar prison, when the guard puts his hand inside the cake, his sleeve is by his wrist or rolled up to the elbow, depending on the shot. (00:03:10)
Continuity mistake: After the bug in the cake kills the cops, it runs to free Boris. The amount of strawberry cake on the sewer lid changes between shots. (00:03:25)
Continuity mistake: When Boris blows the prison door and encounters hundreds of guards, the damage on the door changes between shots. (00:04:50)
Continuity mistake: As K is asking the little boy what his name is, the boy's arms are down at his side. As the camera cuts and he says his name is James, his hands are suddenly fiddling with his shirt tail. (01:33:35)
Continuity mistake: When K takes the prize out of the Crackers box, the size of the box magically becomes very tiny. (01:07:55)
Answer: Earlier in the movie, the way K was talking about Boris was different than what J had come to expect of his partner. So J wanted to know what happened between Boris and K at Cape Canaveral that changed him. So more of what did Boris do to K rather than just the report of what K did.