Audio problem: When Rambo rides the motorcycle down the sidewalk he's shouting at the pedestrians to look out. The movements of his mouth don't match what you hear him say. Originally Rambo was swearing but this was changed.
Audio problem: When the Colonel arrives at the tent we hear the Sheriff say "We're a little busy this morning Colonel, what can I do for you?", but the movement on his lips does not match what we hear.
Audio problem: In the scene after Rambo holds the knife to the Sheriff's neck, we see the sheriff in the tent having his neck looked at by the doctor. The other guy, Dave, says that Rambo is now his problem. The Sheriff then replies, but the movements of his mouth do not match what he says.
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.
Audio problem: After Rambo turns onto the dirt and rock road, it looks like he is shifting gears, but the sound of the engine doesn't match.
Audio problem: In the shot early on, where Teasel jumps his car and breaks a fence post, his car horn beeps when the car lands on the ground. A few shots later, when his car falls down, then flips over on the embankment, the car horn gets stuck. It's a totally different car horn sound this time.
Chosen answer: No he doesn't kill anyone. He didn't know if he was surrounded or not and if he did encounter one from the side they might have shot him.
Grumpy Scot
Rambo killed Galt, albeit indirectly and unintentionally. In the US, "manslaughter involves causing the death of another person in a manner less culpable than murder." Rambo was responsible for throwing a projectile that struck the helicopter, causing the pilot to lose control resulting in Galt falling to his death.
But if Galt had been buckled in, he'd have lived. He was behaving recklessly. Yes Rambo's rock was involved, but that's two steps removed from Galt's death. Rock thrown -> pilot overreacts -> Galt falls because he wasn't strapped in properly. Galt's own behaviour and the pilot's reaction are more at fault than Rambo. This isn't a court, by most reasonable standards Rambo didn't kill Galt.