Revealing mistake: At Coney Island, K zaps J's neck with a tazer and knocks him out. J is seen falling onto his back on the ground, where the background fades out to show time passage that he wakes up sitting in a chair in MiB head quarters. The effect was cool, but the way it was done reveals itself. J wakes up in a leaning back seated position looking up as his head is slumped back over the chair. It is obvious they used this part of the footage to show him lying flat on his back on the ground at Coney Island, only you can tell he is not lying flat on his back. (00:42:55)
Revealing mistake: When the movie starts and J is about to neuralyze the people, the skyline on the background is a blatant backdrop. (00:06:10)
Revealing mistake: During the time jump, there are several points in which it is apparent that J has been animated. (00:36:05)
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.