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.
Continuity mistake: When Packard is pointing a gun at Randa it changes design between shots.
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.
Continuity mistake: In the beginning while Marlow struggles with the Japanese guy he's face down but in the next second is suddenly face up.
Continuity mistake: While Randa and Brooks are following Willis at the hall, there is a woman in red that passes by but in the next shot disappears.
Continuity mistake: At Packard's office, there is a brown cylinder piece that changes place between shots.
Continuity mistake: Before Mason gets in the plane she has her hair behind her neck, but when she talks with Packard she has it on the side and then back behind her neck again.
Continuity mistake: At the beginning before Marlow gets into the jungle he's wearing a yellow jacket that disappears.
Continuity mistake: At the time Marlow lands on the island the sun shines like it's noon but after he gets into the jungle the sun is lower, like it's dawn.
Continuity mistake: After Kong has destroyed all of the helicopters, Cole opens a tin of meat that is full to the top when it is first opened. But in the next shot, he takes one spoon full, and the tin has much less meat in than before.
Continuity mistake: When Col Packard shoots the "ugly bird" he is aiming left handed but after he shoots he is holding the weapon right handed.
Continuity mistake: When Weaver is on the top of the rocks to fire the flare gun to signal the boat, she is wearing her camera/tote bag around her and you can see it on her when she fires the flare at the skull crawler but when she is knocked off the rocks and falls backwards into the water, she isn't wearing the bag.
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