Continuity mistake: While Kong kills the pterodactyl Jack arrives to save Ann. Shot changes and he's back in the cave making his entrance again.
Continuity mistake: The two villagers that are stomped by Kong's foot are bald but grow an afro in the close-ups.
Continuity mistake: A villager jumps off a hut and lands on the floor. A shot later he is 10 meters further ahead. (01:15:06)
Continuity mistake: Kong keeps changing styles throughout the movie at least 4 times: In the close-ups of its head it either has a round face with dirty teeth, fangs and small nostrils or white teeth with no fangs; as opposed to the full body models where it swaps between a cone-head forehead with small nostrils, and a rounder one with larger nostrils, both models with pearly white teeth.
Continuity mistake: The right cuff of Kong's shackles disappears from his wrist when he destroys the train, only to reappear later on.
Continuity mistake: When Ann watches Kong fight the dinosaur, her position is inconsistent between the wide shots and the close-ups.
Continuity mistake: When Kong brings Ann's bed towards him, the footboard changes between the wide outside shots and the inside shots.
Continuity mistake: The planes that attack Kong have two parallel wings, the lower wing being shorter. In the close-up of the planes next to Kong both wings are the same size.
Other mistake: When the planes attack Kong, for a brief moment the superimposed footage of the staircase below jumps to the left. (01:32:47)
Revealing mistake: When Kong is about to attack the train, the building on the right (a superimposed projection) wobbles like jelly for unknown reasons. It's not because of Kong's footsteps, for it never happens in any previous scenes.
Continuity mistake: Kong breaks the window and Ann starts to shout and extends her right leg. A shot later it's bent downwards.
Continuity mistake: Kong breaks the window and takes Ann from bed. In the wide shot (where she's replaced by a stop-motion doll) she faints backwards. In the immediate close-up she is conscious and upright.
Continuity mistake: After Kong escapes from the theater, a car crashes against a wall with no glass on the windshield. In the next shot, broken glass appears.
Revealing mistake: At the Empire State, Kong extends his arm to grab the woman. Problem is, instead of catching her she magically flies up the air to his hand.
Revealing mistake: At the Empire State, the woman is an obvious square-shaped footage of film pasted on top of the footage of Kong. After the plane attacks Kong and his right arm goes limb it goes behind the pasted footage.
Continuity mistake: During King Kong's rampage on the island, he fights some of the natives on a scaffold platform. He picks up one of them and puts him in his mouth. In the wide shot, the native's feet are on the left side of Kong's mouth and his head is on the right. The close-up shows that his head is on the left while his feet are on the right.
Revealing mistake: When Kong is rampaging through New York there are women shown in a window on the upper right. If you watch that was on a loop because they keep doing the same thing over and over.
Revealing mistake: When the men are running away from the Brontosaurus, it is quite obviously sped up. (00:56:40)
Continuity mistake: During the fight between Kong and the dinosaur, the shape of the tree Ann is on differs between shots.
Continuity mistake: Kong shakes the sailors off the log and a man falls down. A shot later he's back on the log. (00:53:12)
Answer: It's never shown or explained, and the film uses a broad "suspension of disbelief" premise. The audience just accepts the characters were able to somehow transport a huge ape to New York City.
raywest ★