Visible crew/equipment: Towards the end of the movie, the Predator is climbing up the side of a tall building. Danny Glover jumps in his car to take off after it. As he starts to drive away, towards the left you can see the shadow of an elevated cameraman/equipment.
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.
Other mistake: In the slaughterhouse scene, after Harrigan has injured the Predator with his shotgun and Keyes reappears, the Predator throws its disc, and severs Keyes in half at the waist. We see his legs flop to the ground, and blood pour from above, but his upper half (torso, backpack and weaponry) mysteriously remain hovering out of sight.
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.
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.
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.
Revealing mistake: When the predator fires his plasma caster in the slaughterhouse scene, you can see that the simple laser blast has been replaced by a Chinese sparkling firework on a string. In the original "Predator" you could see this same effect on a string but it was not nearly as spectacular and easier to miss.
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 30 stories up dangling from a ledge. The slaughter house wasn't 30 stories tall...it wasn't even three stories!
Character mistake: When Harrigan is watching the surveillance video by Bill Paxton he states that the helicopter is a silver Alouette when it is actually an AS-350.