Continuity mistake: In the scene where Ann is unconscious, Kong puts Ann on the ground and she is lying on her arms. When it cuts to the shot when he begins poking her, one of her arms is stretched out.
Continuity mistake: When Ann and Kong are on top of the Empire State Building near the very end, he sets her down on top as he grows weaker. She begins to stand, pulling herself up on his fingers, the shot cuts and she is standing but his hand is now out of place back towards his body, not near Ann where it should be.
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.
Factual error: Naomi Watts is recruited for a role partially because she is a "size 4". In the 1930s there was no such thing as a "size 4". The standardization of women's sizes in the US (i.e. Assigning even numbers to a set of bust, waist, hip measurements) did not occur until World War II (1941 to be exact). See http://museum.nist.gov/exhibits/apparel/index.htm.
Plot hole: When the group goes into the jungle to save Ann, Englehorn gives them 24 hours before the ship leaves. After the dinosaur stampede, Bruce says that the ship sails in 9 hours. That means it took 15 hours for them to get from the wall to the swamp. Later, during the pit scene, Englehorn and the ship's crew arrive to save Jack, Carl and Jimmy from the insects because Bruce insisted on a rescue. But if they really are more than 15 hours away from the ship at this point, there is no way Bruce could have gotten help that quickly. Same when Jack saves Ann from Kong. It's the middle of the night, but when they get back to the ship, which is definitely more than fifteen hours away from the cliff Ann and Kong were at, it's dawn. They simply could not have gotten through the jungle that quickly.
Continuity mistake: When Kong falls from the Empire State Building, Ann is lying down on the roof. She is barefoot, and her high-heeled shoes are nowhere near her. However, when she stands up in the next shot, her shoes are back on.
Plot hole: The opening debut of Kong in NYC is sold out if we are to believe what it says on the entrance doors. Yet Driscoll was watching a play then changes his mind and shows up at the debut. How did he get a ticket?
Suggested correction: He was there when Kong was captured, one of the survivors even. Even though he wasn't given any credit it's possible he got VIP access, as a thank you.
Continuity mistake: After the dinosaurs fight against Kong, Dwan falls on a lake and runs away while staring at the dinosaur. Several bangs of hair cover her forehead. A shot later, when King shows up her forehead is hair-free.
Continuity mistake: In the scene of the ship and movie crew trying to escape from Kong, Kong smacks the bow of the boat, sending Denham into the water in the long shot, but the next close up shot it's Denham splashing into the water again.
Continuity mistake: When Anne is on the rotten tree branch, trying to escape the giant lizard, there is a large black leaf on her chest, but, in the next shot, it's gone.
Continuity mistake: At the end, planes are attacking Kong on top of the building. They stop when they see Ann up there. At one point she is standing, hugging Kong's arm. The camera angle changes to a wide shot and shows her about ten feet away and standing up from a crouched position.
Revealing mistake: When they are all running from the dinosaurs you can see where they should have been crushed by the massive brachiosauruses. Also when they are running along the collapsing mountainside they are somehow able to float along as the ground is giving way.
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.
Revealing mistake: In the chasm scene, when Lumpy is fighting off worm-like creatures, we can see that his sword is made of rubber.
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.