Continuity mistake: When Ann meets Kong on NYC street, the camera flashes back and forth between them. When it shows Kong, he is surrounded by snow, but when it shows Ann, the street doesn't have so much as a snowflake.
Other mistake: When Ann Darrow is awaiting sacrifice to Kong she is hanging from tight thick ropes around her wrists. However, when Kong shows up he just grabs her and tears her from the plinth. Either the ropes should still be around her arms having been torn from their mounts, or her arms should have been ripped off.
Visible crew/equipment: On Skull Island, when Carl says, "No one has lived here for hundreds of years," the distinctive reflection of the reflector screen is visible in the lens of Preston's glasses, as he looks down; there are other moments in the film where this happens with characters' eyeglasses.
Continuity mistake: When Anne comes out of the lake after fighting with the T-Rexes her hair is all wet, but after Kong has defeated the last Rex and puts her on his shoulder to start running, her hair is totally dry. Same happens after she and Jack crash in the river after letting go of the bat. Next shot you see them running towards the temple and her hair is, once again, completely dry.
Continuity mistake: When Bruce Baxter tries to wiggle his way out of having to get closer to the brontos so Carl Denham can get his scene on film ("Shouldn't there be a stand-in for this?"), the gun he holds that can be seen pointing up over his left shoulder keeps appearing and disappearing between shots from the front and back.
Revealing mistake: Near the end of the film, when people are running in terror out of the theater and into Times Square, you can see that the people are not leaving any footprints in the snow. The snow must have been digitally added to the scene.
Continuity mistake: In the scene where Ann Darrow is brought to the Venture, there is a wide shot where she is walking and observing the ship. On one of the ramps (the closer one to her), there is a man who is carrying something up the ramp. In the next shot, if you look at the ramp he was on, he has disappeared.
Revealing mistake: When Ann is juggling for Kong on the cliff edge she starts juggling at one point. If you look closely, you can see that she is simply moving her hands, and the rocks have been added digitally. This is most obvious when she leans right back, and the rocks don't match her hand movements at all.
Continuity mistake: Note the chrome centers on the wire wheels of the taxi that Jack commandeers towards the end of the film. Initially the left rear one is missing, but it magically reappears later on.
Continuity mistake: Soon after Kong grabs Ann for the first time and is playing with her the wide shots show him violently shaking her around, enough to snap her neck or at least render her unconscious, but the close-up shots during the shaking show her being much more gently rocked from side to side.
Continuity mistake: As Jack Driscoll flees Kong in a yellow cab through a narrow alley, the view through the (missing) windshield shows a pedestrian in light-color overcoat crossing leisurely at the other end. When the car eventually emerges in the immediate next shot viewed from the sidewalk, that particular pedestrian simply disappears.
Factual error: In at least one shot as Kong is on top of the Empire State building, the sunrise over Long Island is wrong. Three planes attack from the southwest and we see the sun rise in the east as Newtown Creek (Nassau River) glistens across the East River. The mouth of this river opens southward but in this shot everything is inverted with the mouth of the river pointing northward. Also, looking eastward, Roosevelt Island should be on the left of Newtown Creek, not on the right.
Continuity mistake: At the end of the chase through the streets of NYC, Kong stops the yellow cab with a "karate chop" to the front-end, which sends the car tumbling high into the air through a complete somersault before it lands back down. Actually, Kong's hand is still half way down and nowhere near touching any portion of the vehicle when its rear-end gets lifted.
Factual error: In the scene where Kong is running around the streets of New York City and being chased by two military vehicles, the lead open-topped sedan has an air-cooled 30 caliber machine gun mounted on a bar behind the driver, with the gunner in the back seat. The time setting of the movie is 1933-1934. Air-cooled ground mounted machine guns were not in general use until 1942, and were not available for aircraft until 1936. The Army used water-cooled machine guns until the start of World War II.