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.
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.
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.
Factual error: All the helicopters shown have wire strike protection systems fitted. They weren't produced until 1979.
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