Continuity mistake: When Col Packard is introduced, one can see on the left side of the desk behind him a wooden object beside a picture. In the next shot that object moves to the right behind the radio, only to return to the picture in the following shot. And it moves after this shot again behind the radio, and then stays there. (00:10:00 - 00:11:00)
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)
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)
Continuity mistake: During Kong's final fight with the giant Skullcrawler, he throws it against a large outcropping. Mason is standing on top of it, and the force throws her backward into the lake along with a sizable shower of boulders and rocks. When the scene cuts to show her sinking unconscious into the depths of the lake, she is alone and there are no rocks or boulders sinking along with her.
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.
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.
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.
Suggested correction: He is referred to by his name "Chapman"; it sounds close to "Captain."
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 Packard is pointing a gun at Randa it changes design between shots.
Factual error: When Lieutenant Colonel Packard meets war correspondent Weaver, it is mentioned that she was embedded with MACV-SOG in Vietnam. MACV-SOG was a top secret group that wasn't officially acknowledged until the '80s. There is no way that they would have allowed a reporter to be connected with them.
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.
Continuity mistake: While Cole is eating his helmet moves between shots.
Continuity mistake: While Marlow is cutting off his beard Nieves is besides him but disappears in the next shot.
Continuity mistake: After Kong saves Mason her body changes position on his hand.
Continuity mistake: When the crew gets to the island, Mason is taking some pics with a soldier behind her that disappears between shots.
Suggested correction: The implication is that Marlow went through an extensive debrief and nobody had contacted his family until the debrief had concluded, based on the top secret nature of the mission. As you say, the fact he has a brand new uniform suggests that he has contacted the US Military prior to ever contacting his family. The fact that his wife would have moved and re-married is irrelevant, he still would have made an attempt to contact her so he could see his son.
BaconIsMyBFF
And they wouldn't have contacted her after the debrief had been completed? What utter nonsense. Allowing him to just turn up on the doorstep without notifying his wife first is an utterly irresponsible and even dangerous act. She could have fainted with shock or even had a heart attack. She would absolutely, definitely, 100% carved in stone, been advised of her husband's survival and return.
Since we know very little about the completely fictional organization Monarch, we obviously cannot say they would "carved in stone" do anything. In order to be a mistake in the movie, it would have to be something that is impossible. A secret government organization that doesn't even exist in real life not behaving the way the real military would is not impossible. At least not by the rules set forth in the film. It's perhaps improbable but it is most certainly not impossible.
BaconIsMyBFF
It is an inviolable, carved in stone, fur lined, ocean going, top of the list rule that the next of kin are immediately advised of the change of status of military personnel. MIA, now confirmed dead? They'd be the first to know. MIA, now confirmed to be alive, same outcome. His wife would know he was on that ship coming home.
This is true in real life but in the fictional world of the movie Monarch is a secret, government agency that has some degree of control over the military. You can't apply the same rules as in real life in this situation.
BaconIsMyBFF