Continuity mistake: Before Kay erases the memories of the border patrol cops, he holds the neuralizer with his left hand while adjusting its knobs with his right hand. In the next shot, he's holding the neuralizer with his right hand.
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)
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.
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)
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)
Continuity mistake: When Edgar/The Bug is drinking water with sugar, the way he holds the glass changes between shots. (00:15:21)
Continuity mistake: During the written test, Hudson accidentally pierces the page with his pencil. He then reverses the pencil so the eraser is towards the paper. After the cut to Jensen trying to work on his, Hudson's pencil is suddenly corrected with the point towards the paper.
Continuity mistake: When J holds the baby squid, his fingers protrude more or less depending on the angle. (00:44:40)
Continuity mistake: In the jewelry store, when J chases the farmer, the boots behind him swap from standing to fallen between frames. (01:03:35)
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.