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: 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.
Continuity mistake: The sheriff left his hat in his upside down car. He suddenly has it at the gorge.
Continuity mistake: When the truck crashes through the police road block, you can see the tailgate coming down. At the gas station, however, it's up again and Rambo has to lower it to get the M60.
Continuity mistake: During the car chase, after Rambo escapes from the jail, the hub caps on the sheriff's car keep appearing and disappearing. The passenger rear and one on the driver's side even pops off, but reappears again. Look closely after the car flips over.
Continuity mistake: When Rambo throws the soldier out of the truck and has a dog fight with the state police vehicle his shoes are shown on the accelerator pedal. Those are shoes, not the genuine army boots he wears in the rest of the movie.
Continuity mistake: When Rambo jumps the fence on the motorbike, Will follows in the car but look at the rear wheels of the car they are bigger and wider with no hub caps because of the rough ground when there back on the dirt road the rear wheels are normal with hub caps.
Continuity mistake: After jumping off the dirt road chasing Rambo, the sheriff's right rear wheel has the hubcap on after landing. A second later, it's missing.
Continuity mistake: During the motorcycle chase, just after the police car breaks through the wooden gate, in the close up of Rambo's motorbike its wheels go through two puddles, a short space of land, then another puddle. Keep watching closely as he rides through the mud. In the overhead shot of Rambo approaching the road at an intersection, he goes through the same three puddles again (the third one is hidden behind a tree, but you can still see the splash).
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.