Visible crew/equipment: When J is going to use the neuralyzer on K, on J's lenses you can notice that K has been replaced with a white screen used for lighting.
Audio problem: When Jay goes to join MIB, he greets the security guard with "'sup pops?" without moving his lips. (00:33:40)
Continuity mistake: The Bug pulls his new "Edgar Suit" skin back tight over his face and the wife faints. In the wide shot, he is still holding it back, but the head is completely normal. (00:15:30)
Other mistake: After Mikey is gone, the guard comes down the embankment. As he does, the background "sky" now seems to have a long multi-story building outlined in it.
Continuity mistake: After D is knocked down, K draws his weapon. In one shot of Mikey running, K has his gun aimed directly at Mikey. A moment later, K is shown aiming at Mikey again.
Revealing mistake: As K walks out from the car, saying "INS, Division Six", look at the road they just drove up. It runs a short distance, and ends at a hill of dirt. Presumably, the pile and the end of the road are at the sound stage wall.
Continuity mistake: When Jay touches the ball that goes flying around, the ball goes past the Immigration Stats board where the time reads 33:01:42 pm. Then when we see the alien surveillance map, the time is 30:21:40 CTN. Then the second shot of the map, the time reads 32:01:42 CTN.
Continuity mistake: In the opening scene, when the van is approaching the road block, you can see the 4 sets of headlights. However, when we see the road block from behind, we see one cop car parked at an angle, in front of another cop car's headlight, which would obstruct the view of the light which we saw before.
Continuity mistake: When K shows the neutralizer at the border patrol guys, he holds it parallel to his face, but in the close-up it's next to where his shoulder meets the arm. (00:07:50)
Continuity mistake: When Arquillian's stretcher is about to pass through the doors, the cat is raised and nervous, when the angle changes he is resting relaxed. (00:50:00)
Continuity mistake: When J is searching for the cab, K arrives to pick him up and says "He won't be leaving in a cab". Right then a bus suddenly appears on the right lane, only to disappear in the next angle. (01:14:40)
Continuity mistake: At the morgue, K walks towards the Arquillian's head while Weaver and J walk to see the Jeweler. When the angle changes, a frame later, K is meters away, close to the racks. (00:52:00)
Continuity mistake: When J exits the jewelry, he falls on a some trash with a pizza box next to his armpit. A frame later, the box is laying by his hip. (01:03:45)
Visible crew/equipment: When J puts the glasses on for the first time, a lighting screen is reflected on the right lens. (00:38:30)
Continuity mistake: After Dr Weaver unveils Arquillian's body, the way the blanket is folded changes between shots. (00:51:55)
Continuity mistake: When Arquillian's body is brought to the morgue, the strap around his legs disappears in the first shot. (00:50:00)
Continuity mistake: Towards the end, when J is fending off the Edgar Bug with the flaming branch, Edgar's mandibles are outside his mouth. Cut to a shot of J and the mandibles are inside his mouth. (01:23:40)
Continuity mistake: After doing his recruitment test, Will Smith and Tommy Lee Jones are sitting down on a bench and talking. The distance between them decreases between the first and second shot. (00:31:20)
Continuity mistake: When the farmer kills the two men at the diner he exits the place and encounters a passer-by. When the angle changes the man has vanished. (00:43:05)
Continuity mistake: When the two men with the cat are eating at the diner, the table behind the old man is either empty or has an old woman sitting by it, depending on the angle. (00:41:30)
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.