Revealing mistake: At the very start of the film, when the car blows up, if you look to the right you can see a piece of debris (it looks like a car door) flying through the air. Look on either side of it and you can see the black cable it's gliding on. (00:02:45)
Visible crew/equipment: Near the beginning of the film when the police car explodes and flips over, you can blatantly see stunt wires used to aid in flipping the car. (00:02:45)
Revealing mistake: The police car that is shot at and flips over doesn't have an engine. (00:02:50)
Continuity mistake: At the start of the film, Glover's character blows away the Colombians with a shotgun outside their drug den. Immediately afterwards we're shown the Predators POV (in thermal vision) - looking directly down at their bodies, which show up a greenish color. This would indicate their body temperatures dropped to a much lower level impossibly fast. (00:07:00)
Revealing mistake: When the drug lord falls from the roof he lands on a table yet it doesn't collapse under his weight. The building was pretty tall. (00:10:25)
Continuity mistake: Shell casings on the rooftop disappear and reappear between shots after Harrigan shoots the drug dealer off the roof at the beginning of the film. (00:10:29)
Continuity mistake: At the warehouse, when Harrigan and the other officers are looking at the carnage caused by the Predator, Danny points out the dead Columbian hanging from the skylight. The camera cuts to show the man hanging dead from the skylight, and you can see that he has a good amount of blood running down his body. When Harrigan is ordered downstairs, the scene cuts again to the body being hauled up by the Predator, except now the amount of blood has increased tenfold, looking almost like someone threw a bucket of blood on the corpse. (00:13:40)
Visible crew/equipment: When the Predator is attacking the Jamaicans in the penthouse, you will see the guy who gets pinned to the wall with the net propelled backwards. We are led to believe that it is the force of the Predator's weapon - not so - it is the bungie cable attached to his trousers. (00:24:55)
Continuity mistake: At the penthouse, the Predator lifts one of the Jamaicans on his wrist blades. Another Jamaican turns to see his friend dangling in the air with a claw sticking through his torso. In the next shot from the Predator's POV, the Jamaican is facing as before and still shooting at the wall like he didn't notice. After that, it shows the same man turning in an arc that should show the Predator, but it and the impaled man have disappeared entirely. (00:25:10)
Continuity mistake: At the penthouse, the Predator stabs a Jamaican with the spear and turns as another man steps out from behind a column. It switches to the Predator's POV and the man does the exact same thing again. (00:25:25)
Suggested correction: This isn't a mistake. This is simply showing both perspectives one after the other. It is quite common to see films do this. Another thing could be that the Predator is simply circling him, forcing him to continually turn.
Audio problem: Right after the Jamaicans are massacred in the office tower, a bunch of reporters are all broadcasting from the scene. The camera moves along a row of them. Their mouths aren't in sync with what they are saying. (00:25:50)
Revealing mistake: When Danny falls down from the ceiling, watch closely and you can see the security wire attached to his leg. (00:34:40)
Continuity mistake: Harrigan goes to the medical examiner to ask her about Danny's body. When he asks about the other bodies, he straightens up as she answers, then he does it again in the next shot. (00:42:10)
Continuity mistake: As Harrigan is walking away from King Willie in the alley, Willie turns toward him to say, "Prepare yourself." His face is well-lit. In the next shot, Willie is facing away in the background and his head is entirely in shadow. He's turned and lit again for his next line. (00:47:00)
Continuity mistake: Notice King Willies teeth before he is killed. They are nasty looking. After the predator cleans up his skull, the teeth are white and shiny and also change size. (00:47:00 - 00:49:00)
Deliberate mistake: When King Willie is confronted by the Predator in the alley the Predator approaches him cloaked stepping through the puddle of water. You can see his footsteps causing the water to splash up. However, you can see the water splash up and go through his foot. The Predator is only cloaked, not intangible so the water should have splashed upon his foot, not go through. Water against his foot would be visible too, even though he is cloaked. (00:47:45)
Continuity mistake: The threatened businessman on the train swings his gun all the way to the right, past the pole. The camera switches to his POV as he swings back, but he doesn't pass the pole again. (00:54:35)
Continuity mistake: In the scene on the subway before the Predator attacks. Bill Paxton's laser sight alternates being on and off every time the shot changes. (00:54:50)
Visible crew/equipment: When Jerry is fighting the Predator in the subway car, watch closely behind him when he runs out of ammo. He bends over to pick up a knife, and you can see two distinct shadows on the wall in the strobing light. One is his, and the other belongs to the camera man standing a few feet to the side. (00:57:45)
Revealing mistake: When the subway train slams on the brakes, the camera cuts to a shot showing the sparks coming off the wheels as the train is slowing down. If you look at the wheels carefully, you can see that the train is already stationery, and the camera is panning down the train to give the impression its slowing down. (00:58:30)