Plot hole: The idea that Marlow would simply take a taxi to his wife's address after being missing in action for thirty odd years is stupid beyond belief. He was on a ship sailing from the central Pacific for days and those ships have radios! The US military would have known he was coming. Someone, somewhere would have notified the authorities that a US serviceman long thought dead was actually alive and on his way home and his wife and son would have been there on the docks to greet him, not standing slack-jawed in the kitchen dropping trays of drinks on the floor when he turned up! What would have happened if she had remarried? Or moved house? Or she was dead? Don't tell me the US military didn't know he was coming - he is wearing a brand new uniform, clean and pressed.
Other mistake: Throughout the film Mason goes through all sorts of shenanigans - explosions, fire fights, falling off a cliff, almost drowning, this woman really goes through the wringer. It's a bit surprising then, that at the very end of the film when the good guys finally come to the rescue that she looks like she has just finished posing for a shampoo commercial with not a hair out of place.
Factual error: In the scene at the Bangkok docks, the ship has the name Athena but with the Greek letter Lambda instead of each capital letter A. This would make the name something like Lthenl, and is a nonsense mix of Greek and English (Roman) letters.
Factual error: Ka-Bar knives with serrations on the blade were not sold until the 1990s.
Character mistake: Chapman is wearing a gold oak leaf cluster insignia on his uniform which is the rank of Major. At the initial briefing he is introduced as Major, which is correct. Throughout the movie he is referred to as Captain, which is wrong.
Factual error: When Packard and his men arrive on the island, they are seen wearing ALICE gear (All-purpose Lightweight Individual Carrying Equipment). The film takes place in 1973, that type of gear would've just finished testing phases in 1973. The soldiers would be more accurately equipped with M-1956 Load-Carrying Equipment (LCE) or M-1967 Modernized Load-Carrying Equipment (MCLE).
Factual error: When she is detailing her military experience Mason mentions she was "embedded with MACV-SOG." The practice of embedding journalists with military units during wartime did not become a formal practice until the Iraq War of 2003. Prior to that many journalists during the Vietnam War, like Joe Galloway who was with the 7th Cavalry at the Ia Drang Valley, had to find their own way to the battlefield. Additionally "embedding" was not a term that would have been used by the military or the press at that time.
Continuity mistake: During the arrival to the island there are 11 choppers. The first time Kong appears he takes down two. In the next sequence where they all see him for the first time 11 choppers still fly by Kong. (00:30:40)
Factual error: In the beginning Packard is in his office and opens a brown cigar box. That is a Rocky Patel box that wasn't developed in the cigar industry until 1995.
Continuity mistake: When the group has just encountered Kong, a visually dramatic scene shows Kong silhouetted against a deep orange setting sun. Yet immediately before and immediately after the scene, the sun is high in the sky and it does not get dark for what would be several hours in the movie timeline. (00:31:50)
Factual error: In the opening scene, Marlow's P-51 Mustang has D-Day invasion stripes. These were used in Europe, not in the Pacific where the movie takes place. Even if the plane were transferred, it would have been repainted.
Continuity mistake: When they kill the big spider, its guts spill over one of the soldiers, but in the next shot, his face is clean.