Visible crew/equipment: During the motorcycle chase Rambo jumps over the train tracks, if you look close you can easily see the ramp. (00:18:00)
Visible crew/equipment: In the shot of the stolen army truck crashing through the police road block, you can see a camera mounted inside the truck. Look in the small window on the rear wall of the cab. (Apparently both this shot and the shots from inside the cab were done in the same take.) (01:13:10)
Visible crew/equipment: At the beginning of the movie, Sheriff Teasle escorts Rambo to the outskirts of town. As the sheriff drives off, the boom mike is visible in the reflection of the car's right rear passenger window. (00:07:30)
Continuity mistake: When Rambo has Teasle up against the tree with the knife, it is under Teasle's throat, but in the next shot the knife is to Teasle's right without Rambo moving it.
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.