During the film, despite Ann getting thrown about and manhandled by Kong, sliding down rocks and cliffs in bare feet, and falling over numerous times to escape the many creatures and dinosaurs, she ends up with virtually no marks or scratches on her body. Her dress gets dirty, but that's about it. Her hair also stays reasonably in place. She would have been scratched and bruised all over her legs and arms from the trauma.
(at around 23 mins) As the ship is leaving its dock in New York the captain orders "dead slow ahead both". This indicates that the ship had two engines and two screws; however, every shot showing the stern of the ship has a propeller wash coming only from the center of the ship, showing that it has just a single screw.
As Kong carries Ann during the fight with V-rexes, Ann's legs sometimes face one direction, and her torso and head are in the opposite direction.
Ann's clothing changes throughout the period on the island when Kong has her; a narrow camisole-strap, a wide flat white shoulder-strap, or the untorn collar/shoulder fabric of her dress are randomly present on her shoulder at various times, and the condition of her clothing changes in how tattered and/or removed it is between shots.
(at around 1h 40 mins) When Ann slides down a muddy slope, her back is covered with very dark mud. When she gets up, her back is clean.
As with a lot of "dinosaur" movies (e.g., Jurassic Park), this shows dinosaurs stop eating a large carcass to chase a small, moving prey like Ann. No predator would stop eating readily available food to waste energy chasing something smaller. That would be like a lion feasting on a wildebeest stopping to chase a meerkat. At most, it would roar at the meerkat to scare it away. This is particularly incorrect when the one has a full body of a dead dinosaur in its mouth and is chasing Ann, who would be equal in size to the hand of the dead one it has.
(at around 2h 50 mins) When Jack Driscoll goes up in the Empire State Building elevator, he watches an old-fashioned dial-and-arrow indicator as it sweeps upward through the floor numbers, from "1" to "101". However, the building's structure does not allow for direct elevators from street level to the very top. The metallic tower topping the limestone façade above the 86th floor observation deck is served by only one small elevator shaft and one narrow staircase - that's all that will fit. A change of elevator is necessary on or about the 86th floor for anyone going to the very top. Also, the top floor is officially "102", not "101".
When Kong captures Ann, he grabs a hold of her and pulls so that the ropes binding her snap. As she is still tied to the ropes and he pulls her body, she would have at least suffered dislocated arms if not broken ones.
With all the ice and long coats during the New York City scenes, one would assume that it was winter and cold. Unless Ann has hidden blubber or fur, she would have gotten fatal or severe hypothermia or, at the very least, a really bad case of frostbite.
Using a submachine gun, firing at full auto, to pick the bugs off someone's back without killing or wounding that person is simply impossible.
(at around 18 mins) 'Surabaya', an Indonesian town, is shown under the name of S.S. Venture. Some people have noted that it was still written as "Soerabaja" in 1933, but the spelling "Surabaya" was, in fact, already accepted in English at that time. (source: The Times of India New Standard Encyclopedia and World Atlas, 1936)
Although there's no official explanation given for the unlikely feat of transporting Kong from the ship and into the Broadway theater without anyone noticing, it is very likely that the process took a very long time, hence the director's decision not to show the audience.
The way Kong shakes and throws Ann around while carrying her would almost certainly snap her neck or spine.
(at around 1h 11 mins) When Ann "meets" Kong for the first time, she is bound securely with some very large pieces of rope around her wrists. Kong hoists her up her waist, snapping the ropes easily. Given the size of the rope, this would more than likely rip her arms completely off or cause her other serious injury (unless the natives were really bad at tying knots).
The Venture crashing into several rocks especially on the port and starboard sides would have been severe enough for the ship to sink rather than stay afloat.
(at around 1 min) At the very beginning of the film, during Al Jolson's song, the camera looks down on a bridge with lots of cars passing it. On the right side of screen, an animated plume of smoke from a chimney is frozen - on the left side animation is working correctly.
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.
(at around 1h 15 minutes) At the end of the sequence where Kong carries Ann through the forest, there is a very brief scene where Ann is wearing pantyhose (not invented until 1959, twenty-six years after the story took place). However, Ann's legs and feet are bare in all other scenes on the island.
(at around 14 mins) Denham asks Ann if she wears a size 4. Commercial standards for clothing sizes were formally accepted in 1957, and they started at size 8.
(at around 2h 45 mins) When Driscoll enters the elevator at the Empire State Building during the film's climax, he reaches over to select a floor, revealing that the elevator features self-service. Elevator operators were still employed in the Empire State Building during the early 1930s.
(at around 1h 50 mins) After Denham drops his camera and the film falls out, it is clearly a modern tri-pack color negative and not a 1930s vintage black-and-white negative. You can tell because of the orange/brown color of the material.
(at around 2h 25 mins) Peggy Lee did not begin her recording career until the early 1940s. Her recording of "Bye Bye Blackbird," used in a nightclub scene, dates from 1955, more than twenty years after the time of the film.
When Ann is in Kong's hand for the first time, you can see a screen bounce behind Ann.
When Kong is shaking the tree down, it's obvious that there's a screen behind the film crew when they fall.
In the chasm scene, when Lumpy is fighting off worm-like creatures, we can see that his sword is made of rubber.
After Kong is captured, Englehorn seems to have forgotten that there was still a warrant for Carl Denham's arrest, as Denham is seen back in New York rather than being imprisoned in Ragoon.
Apparently there was a warrant for Carl Denham's arrest, but Englehorn doesn't get a message about this until the ship is near Skull Island.
The story, as it is told, features a major omission, which would have eliminated the climactic New York scene to have occurred at all. The same way as it happened in predecessor, King Kong (1976). How could Kong possibly have been loaded into the ship in the first place, whether conscious or unconscious? Even worse, off-loaded in the New York harbor, then transported to the theater? A logistical nightmare, no, an impossibility, for no person on this Earth can even visualize how that could possibly be accomplished. Imagine carting that hulk past Times Square. Whether conscious or unconscious.
(at around 2h 20 mins) In New York, Carl Denham states that 17 crew members died on Skull Island. The actual death count is 27.
(at around 1h 35 mins) Before Kong picks up Hayes, he fires a shot from his pistol; then he is seen cocking his weapon again while he is in Kong's hands. He was shooting a semi-automatic pistol, so there was no need to cock the gun again.
Carl Denham tells the board of directors and Jack Driscoll that Skull Island has never been seen before by humans. However, it is likely the person who made the map either lived on the island or more likely discovered the island. So, technically, Carl would had lied the island was not discovered. (Not to mention, of course, that the island is inhabited, so it has obviously been seen by humans.)
Lumpy says 4 men died in the stampede. Actually, at least 5 people died in the stampede; six if you count a deleted scene. Either way, the sixth man is present before the stampede but not when they regroup afterwards, and so can be inferred to have died.
When Ann is talking to Carl at the table before accepting his offer, she briefly says some words in an Australian accent and not American.