Revealing mistake: When Bill Duke picks the scorpion off Carl Weathers' shoulder with a knife, you can blatantly see some gum or similar that's been used to stick the scorpion onto the tip of the knife. Even if it's meant to be Bill Duke's gum, it's not on the tip of the knife before he stabs it.
Revealing mistake: After they catch the Predator in the net and it breaks free, the laser blast breaks a big part of a tree and it heads toward a soldier, hitting him head on. If you watch closely when they show an above shot of the tree hitting the guy, you can see an air pressured pad pushing the tree on the ground into him. (01:06:40)
Visible crew/equipment: During the final battle, shortly after Dutch runs by a plant that moves and catches the Predator's eye, watch as the Predator takes a few strides from rock to rock. When he jumps down off the last rock you can see a cable above his head helping him make his jump. This same cable can also be seen from a different shot about ten seconds later when Dutch runs into the Predator. (01:29:45)
Revealing mistake: When Arnold is heading into the trees after building his bow and arrows you can see a silver eye bolt on the top of the bow where the string would attach.
Visible crew/equipment: When Arnie says 'oh s***' and falls off the cliff, watch as the camera goes over the edge. If you look on the mountain, you can see a shadow of a black ball with a cable attached: this is the camera filming the shot which has been thrown off the cliff.
Visible crew/equipment: Watch when Arnie is sliding down the cliff: it shows a shot from his eyes looking down at his feet, and you can see the wooden platform he's sliding down.