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: At the end of the fight in the slaughter house, Lt. Harrigan scrambles up a ladder and goes onto the roof with the predator in hot pursuit. A few moments later, Harrigan slams into the predator and they both fall off the roof. Suddenly, they are about 10-15 stories up dangling from a ledge. The slaughter house wasn't 10-15 stories tall...it wasn't even three stories. (01:16:05 - 01:24:25)
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.
Continuity mistake: At the very end, as Harrigan says his last line, he lifts the pistol over his shoulder in his right hand. Cut to the helicopter taking off and both his hands are lowered, with the pistol in his left. (01:41:05)
Continuity mistake: As Harrigan approaches the collapsed Predator in its lair, he switches from holding the disk at an angle to holding it flat. (01:35:25)
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: When the Predator snatches the skull with the spinal cord attached from Bill Paxton's body in the subway tunnel, there should have at least been small amounts if not a good bit of blood left on the stairs leading up to the street surface by the time Danny Glover go to it while he was chasing him. (01:03:05)
Continuity mistake: On the end of the movie, when Harrigan is leaving the cave where the alien ship was, there is no way a ship that big could pass through such a small hole. (01:39:00)
Continuity mistake: In the slaughterhouse scene, Danny Glover's character pulls out a shotgun and blasts the Predator several times, knocking it flat on his back. Just as soon as you see the Predator hit the ground, you can see his mask start to fly off as though it's loosely attached. In the next scene, Danny Glover has to put some effort to pry it off, when it should have flown off in the first place. (01:18:45)
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)
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)
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: In the beginning, after the gang retreats into the building, you see what appears to be the leader sniffing from a golden container. After a quick cut to the gang getting ready, you see his moustache covered with white powder. After another cut, a closeup shows his moustache is clean, way too quick to have cleaned up.
Continuity mistake: After king Willie has had his head cut off, the marks on his cheeks are much darker and drawn on with marker pen. Otherwise, the decapitated head is quite convincing.
Continuity mistake: Harrigan blows his way into the slaughterhouse with a series of explosions. The Predator whips around as soon as it hears the first one, then does it again after a few more explosions go off. (01:16:15)
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)
Continuity mistake: When the Predator finally collapses at the end, Harrigan rises out of the mist on the ground twice. (01:35:15)
Continuity mistake: At the end when Harrigan is walking out of the tunnel and the helicopter is preparing to land the pistol is in his right hand, but after that as the helicopter lands he's holding it in his left. (01:40:26)
Continuity mistake: When the Columbians are in the armoury near the beginning, they all look up as a skylight shatters. In the slow motion shots, you can see the leader turn away from the glass. But, then it shows him in a closer shot, and he's still facing the falling glass, and falling back away from it, shielding his face with his hands.