(at around 1h 15 mins) At the end of the sequence where Kong carries Ann through the forest, there is a very brief scene where you can see that Ann is wearing pantyhose (not invented until 1959, twenty six years after this movie took place). In all other scenes on the island she is barefoot.
(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.
The on screen camera and sound recording gear depicted in the film bear no resemblance to the mass of equipment; mixers, recorders, lead-acid batteries, heavy cables, generators, and tens of thousand of feet of film (ten minutes worth weights 5 pounds) required for a location sound production (even a documentary) in the period the film is supposedly set. Sound cameras were never hand-cranked but instead, electrically driven from the same generator that connected to the sound recorder in order for them to stay in sync. And the sound recorder, then called a sound camera employed a photographic rather than magnetic recording process, which didn't come in to common use until after WWII.
(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 tripack color negative and not a 1930's vintage black and white negative. You can tell because of the orange/brown color of the material.
(at around 11 mins) Before leaving port, Denham tells his asst. to pack "Red Label 80 per cent proof" into a crate labeled "lemonade". At present, Johnnie Walker Red Label scotch sold in the US is 80 proof (meaning 40% alcohol). However, until the late 1980's and early 1990's, almost all blended scotch sold in the US, including Red Label, was reduced from 86 and 86.8 proof (or 43% and 43.4% alcohol) to 80 proof (or 40% alcohol). Though numerous single malts are still 86 proof, from 1909 into the 1980's, Red Label, which is a blended scotch, would have been at least 86 proof. Denham's mistake of saying "per cent proof" is a natural mistake that the character may have made, and may even have been intended by the writers, but referring to Red Label as 80 proof back in the 1930's is a definite goof.
(at around 2h 30 mins) The Yellow Cab Jack Driscoll takes to lure Kong away has license plates dated 1932. The film is set in 1933, so the cab would have been operating without a valid, legal registration.
(at around 1h 35 mins) Before Kong picks up Hayes he fires a shot from his pistol, then you see him cocking his weapon back 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.
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.
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 8 mins) When Ann is being sacrificed to Kong she is on a greased platform that her bare feet are slipping on as she is struggling. When Jack arrives to rescue her he runs to the end of the same platform. When he reaches the end of the platform he has no trouble stopping.
When T-Rex is chasing Ann through the woods she slips and slides down a muddy hill getting mud all over her back, arms and legs. When she gets up she has very little mud anywhere on her body. Then when she makes it out of the woods she is totally clean but her whole outfit is a shade darker.
(at around 1h 29 mins) After the scene with the Brachiosaurus, Bruce Baxter has a conversation with the main character, Jack Driscoll. During the conversation, the rope on Baxter's shoulder disappears.
(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.
(at around 2h 30 mins) When Kong is chasing Jack Driscoll, you see a shot of an alleyway with a woman in white walking across the alleyway. The camera cuts to the opposite end of the alley, and the woman has disappeared.
(at around 1h 24 mins) During the brontosaur jostling scene in the canyon, Bruce Baxter's character is threatened by a velociraptor standing just above his head. Seen from above, Baxter's reaction is to turn to his right, yet on the next shot we see him turning to his left.
(at around 1h 17 mins) After forbidding Jimmy to join the search party for Ann, Hayes discovers Jimmy with the party by pulling off Jimmy's hood with his right hand. But, on the next shot, Jimmy's hood is pulled off by Hayes' left hand.
(at around 1h 43 mins) The T-Rex is chasing Ann Darrow with a medium-sized monster, possibly a raptor, in its mouth. The T-Rex tosses the raptor to the side and in the next frame or two, the raptor is again in its mouth.
(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".
(at around 18 mins) In one scene, it is shown that there is a name of the town of 'Surabaya' (Indonesia) under the name of S.S. Venture. Some people have noted that it was still written as "Soerabaja" in 1933, but in fact the spelling "Surabaya" was already accepted in English at that time. (source: The Times of India New Standard Encyclopedia and World Atlas, 1936)
Given the presence of snow and people wearing heavy coats in the streets of New York City, it is very unlikely that Ann would have survived climbing to the top of the Empire State Building while wearing a sleeveless white dress. She would have died of hypothermia within the first few minutes.
(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 very easily. Given the size of the rope this would more than likely rip her arms completely off (or cause her serious injury). (Unless the natives were really bad at knot tying.)
(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.
(at around 24 mins) When leaving New York, a 360 degrees shot is taken of the boat by night. However, the shape of the plume of smoke coming from the chimney does not change with the camera's point of view.
(at around 2h 45 mins) When Kong is on top of the Empire State building, and is shot by one of the bi-planes, you can clearly see two bullet holes and blood coming from his chest. The wound immediately disappears.
(at around 2h 55 mins) When Kong falls off the Empire State Building at the end, the ladder on the side of the Empire State Building's dome is in front of Ann, below Kong's chin. But when Kong falls off we cut to a rotating shot from above as Kong falls down, and the ladder is gone. Then Jack climbs up the ladder behind Ann.