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)
Men in Black (1997)
Directed by: Barry Sonnenfeld
Starring: Tommy Lee Jones, Will Smith, Vincent D'Onofrio, Rip Torn, Tony Shalhoub, Linda Fiorentino
Revealing mistake: When Will Smith throws a rock at the escaping Edgar alien, if you watch the rock after it hits the alien, it disappears after hitting the ground. (01:23:20)
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)
Trivia: In many European countries, as in Spain and France, since Dennis Rodman's weirdness isn't that well known, the celebrity mentioned in the last line of the movie as being an alien was changed to Michael Jackson. (01:30:00)
Trivia: After reading the script with his wife, Barry Sonnenfeld (the director) turned to his wife and said "Tommy Lee Jones". She turned to him and said "Will Smith", and that is how they were cast. This is confirmed by Barry Sonnenfeld on the DVD commentary.
Beatrice: I'll tell you something right now; I know Edgar and that wasn't Edgar. It's like something was wearing Edgar like a suit. An Edgar suit.
Large cop: If you were half the man I am... [Jay looks pointedly at policeman's stomach] I am half the man you are!
Kay: Imagine a giant cockroach with unlimited strength, a massive inferiority complex and a really short temper is tear assing around Manhattan in a brand new Edgar-suit. That sound like fun?
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 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?
Answer: Yes, "the Great Attractor" can refer to a specific anomaly in the Centaurus Supercluster, but that is a far cry from saying that the term can only refer to that specific anomaly. It is completely possible for a high-tech prankster and/or performer to use the name "the Great Attractor." It's like saying "the Boss" when referring to Springsteen. The term means a manager over a group of people in a place of work, but he can still use it as a stage name.
Answer: K and his partner both knew about aliens living on Earth, and made it their duty to make sure no one else knew about it. When the trooper saw Mikey in his real form, and Mikey spotted him, he attacked the trooper in an attempt to kill him, probably to ensure that the trooper wouldn't be alive to expose them. Since K and the other agent were already aware of Mikey, as they had dealings with him before, Mikey didn't attack them.