Audio problem: When Will Smith is looking at the two space ships at the MIB headquarters, if you look in the background Zed and K are there typing on the computer. But if you look closer you can tell that they're not even touching the keyboard and the sounds are just added into the movie. (01:16:00)
Continuity mistake: Just before the diner scene, where the two aliens are discussing the galaxy, we see the outside of the Russian restaurant. The neon sign says "haroshaya" meaning "good" all the way across the window, in the next shot inside the restaurant, the "ha", which looks like the English letters "xo", is gone and the sign is centered. (00:41:00)
Question: When we first see MIB headquarters, K says that the little destructive energy ball thing is "a little practical joke by the Great Attractor." As far as I can tell, the Great Attractor is just a gravitational anomaly, so how could it play practical jokes?
Question: When K and J are about to leave the police station, J says that he has a report to do. At that moment, his boss arrives and tells him he did a good report. Who did his report? It couldn't have been the MIB, because J was the only person who saw the entire chase.
Question: When I watched both films in succession, I noticed the same person played both the man on desk at the morgue and Newton, the video store owner in the second film. Is there a reason for him being in both films?