Revealing mistake: When the men are running away from the Brontosaurus, it is quite obviously sped up. (00:56:40)

Revealing mistake: After King Kong destroys the train track of the oncoming train, in the POV shot directly behind the train operator while he watches Kong rise from the broken track, the small model's support control bar is visible at the right as it moves up and down. The next shot is a close-up of the shocked motorman, and after he attempts to stop the train, there's another shot facing Kong with the control bar visible for a moment. (01:31:50)

Revealing mistake: While King Kong is atop the Empire State Building, the biplanes are strafing their large target. There are several static close-up shots facing a biplane's nose, and in these "aerial" shots, there's a girder beneath the set prop's fuselage. (01:36:10)

Revealing mistake: In the last third of the film just after the announcement that Kong is coming, a native jumps out of his hut, loses his balance and falls by a chicken coop. His wig comes off and gets caught on the fence.
Revealing mistake: As the men walk past the downed stegosaurus, the camera moves faster than they do (judging from the background) but they stay at the center of the screen. Obviously the camera on the model of the stegosaurus moved faster than the camera on the men.
Revealing mistake: As one plane swoops at King Kong on the Empire State Building, another flies behind his head that is much larger than it should be relative to him.
Revealing mistake: The figures dropping from Kong's cliff into the river are obviously limp dummies.
Revealing mistake: When Kong crushes the scaffolding in the island village, it collapses not into a heap of splinters but in a neat panel of solidly bound wood.
Revealing mistake: When Kong breaks through the giant doors towards the islanders, part of the doors become transparent and you can see Kong's leg. This is a result of the matting special effects used.
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 sea creature appears and the raft overturns, the people falling are very obvious stiff dummies. One even falls downwards and its two feet stick up from the water.
Revealing mistake: In New York, when Kong abducts and kills a woman, and later abducts Ann, there's a shot of the street below. It is repeated all the time, sometimes flipped, with varying light intensities.
Revealing mistake: When Kong strips Ann, it is a composite of two images: footage of a huge mechanical arm holding her and a puppet Kong in a miniature set. The arm footage is noticeable because the background wobbles, and the pasted area stands out from the miniature set behind.
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.
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.
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 ★