Revealing mistake: When Kong arrives at the top of the tower, his foot clips through the railing footage.
Continuity mistake: When Kong swings the log, the man in the middle falls down and holds onto a branch. Barely a second later, he is standing up again and repeating the previous fall.
Continuity mistake: Kong throws a barrel at the soldiers, and Jack shouts, "Yes!" Then he rests his left hand on the wall. From the immediate opposite angle, his hand is now fisted. The hand's position is also inconsistent in the following shots.
Continuity mistake: When Wilson falls inside Kong's footprint, his scarf swaps between tied around his neck and loose back and forth between shots.
Revealing mistake: The flamethrower scorches Kong, who is behind an antenna. However, the antenna remains perfect, revealing it is a projection.

Continuity mistake: Inside the cargo hold, Kong throws a pipe on the floor. In the aerial angle, it's gone.
Factual error: When the Petrox engineers dump Kong into the pit filled with chloroform they haven't knocked him out - they've killed him. Chloroform vapour is heavier than air so Kong is breathing it in a pretty pure form - and it is lethal in concentrations as low as 40,000 parts per million. In the time it would take to render a gorilla unconscious by this method, it would die. This ignores the fact that liquid chloroform is a severe irritant and a contact poison, and its breakdown products include phosgene and hydrogen chloride, both deadly poisons. They might as well save themselves some time and use that dinky little bulldozer to fill in the pit.
Factual error: The fact that the respiration of a single animal - however large - could lead to an increase in the level of carbon dioxide in the local area is so absurd it is laughable. Carbon dioxide exhalation is part of a closed loop cycle and the CO2 exhaled by Kong would be matched by the CO2 taken in by the plants growing on the island. It cannot be otherwise. Elevated levels of carbon dioxide are incredibly dangerous and any animal living on the island - including Kong - would suffer if things got out of kilter.
Continuity mistake: When Kong is lying in the hold of the Tanker, Jessica Lange's character is leaning over looking at him when her scarf falls off. When it lands on Kongs chest, it appears to be the size of a (very) large dinner table cloth.

Visible crew/equipment: As King Kong jumps from one of the Twin Towers to the other, you can see the wires attached to him as he lands. (01:59:30)
Revealing mistake: When Kong first shows up to take Dwan away, he roars and pounds his chest. As he does so, the breastplate in Rick Baker's costume vibrates visibly in a way that a flesh-and-blood chest wouldn't.
Factual error: How does Kong return a radar signal? If organic material is suddenly detectable by ship borne radar, why isn't it picking up the trees and other animals? Did someone invent gorilla-detecting radar?
Factual error: When Kong falls in the pit containing the chloroform and passes out, you can see some of the boat crew members walk into the chloroform cloud to look in the pit. Wouldn't they pass out also?
Revealing mistake: Near the end Kong rolls off the top of the World Trade tower. It cuts to a shot from the ground looking straight up toward the top with Kong falling downward. For a fraction of a second there is no image of Kong composited into the shot: first there's just buildings, then suddenly Kong appears from nowhere in midair.
Continuity mistake: When the group of natives has discovered the Petrox crew and begins approaching them, a closeup shows Dwan moving from a crouching to a standing position and nervously taking a few steps back to stand behind Jack. The camera then switches to a long shot and she again stands up and moves behind Jack.
Factual error: When Kong breaks free in New York, he stomps on people, but not an inch of blood appears.
Continuity mistake: Dwan asks Kong, "I bet you are an Aries, aren't you?" with both of her hands lowered. A shot later, her left hand is on her head. (01:02:48)

Continuity mistake: When Kong meets Dwan, he approaches his hand facing downwards. A shot later, it's sideways.

Deliberate mistake: When the natives abduct Dwan, they grab her and leave in a nanosecond, leaving nothing on the deck. When Jack arrives, there's suddenly a necklace on the deck which helps him figure out what went on, despite being a ludicrous and deliberate McGuffin. Check the beer can and red box as a reference.

Continuity mistake: Before Dwan is abducted, the platform where she is fishing is fully lit and has objects scattered everywhere. After Jack leaves, the place is tidier and in the shadows.