Continuity mistake: When Berenger and Zane are at the village where the dead priest is, they see his hut. They move around the hut's door in a police/swat style way, to make a surpise attack on whoever might be inside. But when we cut to an inside shot of the hut, you can see there are spaces in the bambo/stick walls. Even if there was a person inside, they would easily have seen them moving around outside.
Continuity mistake: When the helicopter lands in the LZ to pick them up at the end of the movie, its position and anti-collision lights are on. Not a smart idea, for a night extraction when guys with guns are looking to shoot at you. In the next scene, the helicopter flies away and all the lights are off.
Continuity mistake: When the Surgeon is torturing Beckett, Beckett's arms are about shoulder width apart tied to the bamboo. A couple scenes later, his arms are tied further apart. This makes it really odd because the Surgeon was cutting his finger, which is about a foot away from where he stands up.
Continuity mistake: When Billy Zane is in the helicopter, he sights the sniper in his scope, the sniper being the one that just shot the chopper up. You see from the scope's view that the chopper is apparently following him running down the mountain. But, the helicopter was hovering, it wasn't following him.