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)
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.
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 ★