Continuity mistake: When they're in the jungle in Panama they see a train go past which has the Queensland rail (in Australia) sign on it.
Factual error: In the opening sequence, the range for the shot is confirmed as 650 yards. Moments before the shot, AFTER he had his target centered in his scope, Berenger swings the muzzle of the rifle at least 10 degrees. At 650 yards a change of only a single degree in the angle of the muzzle to the target would mean that the target would have to move 11.34 yards laterally in order for the shot to hit. If Berenger actually had to swing his rifle ten degrees in the span of a second in order to keep his target in view, that would mean the target was sprinting at a speed of 340.32 feet per second, or about 232 miles per hour, and had covered 113.44 yards during that time. Absolutely impossible.
Continuity mistake: In the beginning, when Tom Berenger and his spotter are trying to get on the chopper, the spotter gets shot. First, they show blood on his face. In the next scene it is clean and in the scene after that is it bloody again. The appearance of his wound changes too.
Factual error: When in the helicopter the red dot from Miller's sights stays motionless on the EXACT same spot on the man's back - impossible from a helicopter. Doubly so if compared to the scene at the lake, where Miller is sitting totally still and the red dot is moving back and forth over the swimming guy's head.
Continuity mistake: When Billy Zane slides down into the river, the overhead shot shows him (or a stunt double) completely go into the river. But the next shot, Billy Zane magically keeps his rifle and his upper body dry and above the water line.
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 Miller shoots El Cirujano, who was torturing Beckett, it's a rainy night. In the side shot of Miller's fired bullet, in the background there is a definitely daytime forest, then in the next shot, it's night again.
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.