Continuity mistake: When Rambo is driving the army truck he rams the police car off the road. In the shot just before the police car hits the stationary car the passenger side windows are open and police are shooting at him through these windows. But in the next shot just before the explosion the cars windows are closed.
Continuity mistake: When Deputy Galt falls off the helicopter, the close-up shot reveals he still holds his rifle. A split second later (distant camera), you would expect to either see him still holding the rifle or see the rifle falling away from him. However, the rifle has disappeared.
Continuity mistake: When Rambo is being pursued through the forest and comes upon the cliff edge, the water at the bottom of the gorge changes direction of flow several times. It is first seen as flowing left to right, from Rambo's point of view. The very next shot shows the water flowing right to left. It reverses direction twice more in subsequent shots. (00:24:00)
Continuity mistake: At the onset of the film in the police station, Rambo has a few days of facial hair (also evidenced by the fact Teasle and the other officers 'wanted to shave him'). After Rambo escapes and a few hours later is about to start climbing down the side of the mountain after he hears the other officers and dogs closing in on him, look at the close-up shot of his face just as he looks back and sees that the tracking dogs are very close. Rambo now appears clean shaven. Highly unlikely he stopped to shave.
Audio problem: In the helicopter scene when deputy Gault is telling the pilot "If you don't fly this thing right...." it would be impossible to hear him over the sound of the aircraft without yelling, yet Gault speaks in a normal voice.
Continuity mistake: The rock thrown by Rambo at the helicopter doesn't actually break the windshield at all. For a very short instance (one or two frames) you can see the rock bouncing off the windshield which is still intact. The next frame is cut in (just look at the position of the pilot in the background) - the glass is now broken. Some shots later, when Galt has fallen out and the helicopter leaves, the windshield is intact again.
Continuity mistake: The sheriff left his hat in his upside down car. He suddenly has it at the gorge.
Factual error: The military cannot be used to help execute civilian law except during emergencies. Rambo could, I guess, be considered an emergency however, once the national guard was called out, they would have had jurisdiction over the Podunk police department. When Brian Denehy told them to wait for them, and then subsequently to clean up their mess, he would not have been in charge at that point.
Continuity mistake: When Rambo is hanging from the cliff, and the officer is shooting at him from the helicopter, the cliff he is hanging from with his two arms change just prior to his jump. You see two different ledges he's hanging from, one is a totally even horizontal cliff, the 2nd is a V-shaped ledge.
Continuity mistake: During the chase, when Rambo escapes from jail, the police car jumps and the back hub-cap flies off. The next time you see the the police car all the hub caps are on. And when the police car goes through all the mud in the field, the back end of the car is all muddy, but a few seconds later it is all clean again.
Visible crew/equipment: When Rambo is jumping down to kill the boar, the camera angle is from ground up, you can see Rambo is wearing some type of white underwear over his jeans, most likely a Jock support underwear. During other scenes the brown tarp he is wearing hangs low so you can't see the white underwear.