When Kong first comes in during the "sacrifice" ceremony, he knocks down trees all over the place. During later shots of this same area during the movie, there are no downed trees. In fact, downed trees are not seen anywhere on the island after this initial scene.
(at around 1h 4 mins) In the early scenes when Kong is first becoming acquainted with Dwan after taking her in the sacrificing ritual, they show Dwan from behind sitting in Kong's hand and she is wearing an arm bracelet, but when she is shown from the front sitting in Kong's hand, she isn't wearing the arm bracelet. It happens during the scene where she calls him a "chauvinist pig ape", then starts punching him in the nose and then she apologizes for it when he gets angry at her.
The pipe that Kong rips off the wall and bends up, as well as the fruit that is dumped onto the floor by the sailors, has disappeared in later shots.
(at around 2h 5 mins) The bent up metal pieces that Kong throws at the soldiers are shaped differently when they land.
(at around 1h 13 mins) When the sailors on the log bridge are confronted by Kong, Carnahan draws his pistol twice: once when they first look up and notice Kong, and again when Jack yells for them to stop firing.
Whilst King Kong is on top of the World Trade Center fighting off the helicopters, he knocks two out of the sky, and you see them go down and hear them crash, but when Kong is seen lying on the ground after he falls, there is no smoke or debris from the crashed helicopters where he is lying. It is possible that the smoke and debris is behind the towers.
Although the story spans several days to several weeks, it is always full moon. The story is timed so that the two significant events (the island sacrifice and the New York reveal and death of Kong) take place on the night of a full moon.
Dwan is found adrift wearing only an evening gown, and appears to be the only woman on board the ship. Later in the voyage, she somehow acquires several very feminine articles of clothing. During the montage, she is shown being given articles of clothing from several sailors and then tailoring them herself.
(at around 1h 29 mins) When Kong is captured and falls into the trap, he falls face first. When he raises his arm out of the ground one last time, it's as if he is lying on his back. It is likely that he rolled over before he finally came to rest.
(at around 2h) When Jack enters the South Tower of the World Trade Center as Kong begins to climb, he enters from the Plaza. Seconds later, he is seen running into an elevator on the concourse level. The plaza level is one floor above the ground floor concourse level where he is seen entering the elevator. Obviously, he descended from the mezzanine down to the lobby, either by stairs or escalator, before entering the elevator.
(at around 2h 5 mins) When Kong is on the roof of the World Trade
Center and being attacked by helicopters, there are many shots where the helicopters can be seen through Kong's head as they fly behind him.
(at around 1h 35 mins) When Dwan falls into the cargo hold, her pants change in color from blue, to gray (especially obvious when viewed against the sailors' blue clothing), then back to blue when she emerges from the hold. This is a special effects compositing error due to the use of blue screen matting; the blue of her pants was affected when the blue screen behind her was removed optically.
(at around 2h 5 mins) Just before the helicopter gunships open fire on Kong, it is possible to see the lights from one helicopter reflected in the safety glass positioned in front of Kong actor Rick Baker. (The scene was filmed on an airfield with real helicopters flying in front of Baker at a distance, and glass was placed in front of him in order to protect him from both the helicopters' rotor wash and the burning hot blank shell casings dropped by the helicopters' Miniguns.)
Right at the very end of the movie, around the closing credits, an extra in the crowd around Kong can be clearly seen waving into camera at the cinema audience, in the lingering ultra-wide over-head shot.
(at around 1h 12 mins) On the log that Kong shakes, white chalk squares are visible, probably denoting the path the actors are supposed to walk along.
Jack says they have a river (the East River) between them and Kong, and the bridges are mined. But Kong is 55 feet tall and there are sections of the East River that are only 40 feet deep or less, meaning that Kong could just wade across.
(at around 28 mins) When the crew of the Petrox Explorer head through the fog towards the island, Perko turns and begins to talk, but Jack's voice is heard.
(at around 2h) When the soldier at the foot of the World Trade Center shouts, "What the hell are those men doing up there? Didn't they get my orders?"
At the end of the battle when Kong kills the giant snake he spies Dwan running off with the hero Jack.
To the left of the screen is a piece of studio equipment that looks like a telescopic light stand.
(at around 1h 50 mins) The World Trade Center towers were not visible from the bar as shown.
The announcer says the event is taking place "across the East River from New York City." Across the East River from New York City is ... New York City. The East River runs between Manhattan and the Bronx on its western side and Brooklyn and Queens on its eastern. All four boroughs are part of New York City.
When Wilson is showing the pictures of the fog bank to the crew, he says the first picture was taken in 1943. Then he says the 2nd one was taken 35 years later. The movie is set in 1976 so the second picture was taken 33 years after the first one.