Other mistake: When Ann Darrow is awaiting sacrifice to Kong she is hanging from tight thick ropes around her wrists. However, when Kong shows up he just grabs her and tears her from the plinth. Either the ropes should still be around her arms having been torn from their mounts, or her arms should have been ripped off.
Other mistake: The ladder at the top of the Empire State Building gets loose because a bullet hits one of the screws. It's not very likely that the five other fixtures would snap just because one got shot away.
Other mistake: When Lumpy's head is getting swallowed he lets out a yell which expels his breath. With his head completely covered, including his mouth, he is able to take a full breath and yell again which would be impossible.
Other mistake: In the scene where everyone gets to the island after Ann was taken and the natives hide, Jack goes up stone stairs to where Ann was strung up by the natives before being taken by Kong, Jack says: "She's gone". But when you watch that scene with Spanish subtitles, he says "She's dead" in Spanish.
Answer: They scared them off with their guns. In the scene where they capture Ann to sacrifice her to Kong, Denham and his men come to rescue her and when they start shooting the natives hide. It's never fully explained but the most likely answer is that they are too scared and have even moved villages or are just hiding really well.