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.
Deliberate mistake: The Messerschmitts have painted yellow fronts, this wasn't done by the Germans until after Dunkirk. Christopher Nolan has admitted doing this deliberately so the audience could tell the difference between the Spitfire and the Messerschmitt during the combat scenes.
Visible crew/equipment: The scene where Spencer throws the boomerang for the first time and misses the bikers they take off running. While they are running from the bikers, there is a shot right before the boomerang hits the bikers where you can see a camera man sitting in the bushes on the left side. You don't have to pause it, but can to see it better. (00:36:30)
Character mistake: Jim Sturgess uses a sentence that contains the word 'me'. He is corrected, being told that the word 'I' would have been correct. However, he was grammatically correct in his use of the word 'me'. The correction was in error.
Factual error: When the bus is shown entering Washington, DC for the competition, the shot shows the bus traveling over the Arlington Memorial Bridge with the Lincoln Memorial in the background. That bridge is on the southwest side of the city. Since NYC is to the northeast of DC, this means that to get to that bridge and enter DC that way, the bus had to drive all the way around the city and then come back in from the opposite direction. Even if the bus driver made a mistake and missed the most direct route into the city from the north, there are dozens of other ways to get to the heart of the city without adding a good 45 minutes to an hour to the trip.
Factual error: Barry Seal is taken with the guys of the drug-kartel in a yellow helicopter. There is an internet address on the side of the helicopter, half covered by the door, entirely inappropriate for the timeframe of the early 80's. (00:17:20)
Continuity mistake: In the opening scenes where he gets his mustang back, he hits the guy who comes over the roof and busts the windshield, but in the very next shot the windshield is pristine. (00:07:45)
Factual error: Dutch police cars don't look like they do in the movie, with their blue and white checkerboard pattern. They had blue and orange diagonal stripes on the side. In this movie, they look much closer to what British police cars look like.
Continuity mistake: When Finn is going to an escape pod to run away, he puts his pack down in front of it, seen again in a later shot. When Rose realises he's trying to run away, his pack has moved itself inside the pod.
Factual error: It is roughly 120-135 dB inside of a C-130, especially one that hasn't been specifically modified. It is so loud that it is painful to be in the cargo hold without hearing protection (besides it being outside of military regulations) and you certainly couldn't have a normal conversation while it was in flight.
Revealing mistake: On the ice the tank is firing - in slow motion we see empty shells are littering the area. The shells have crimped ends, revealing them to be blanks.
Other mistake: Near the start of the movie Jon indicates that he has titanium in his right arm, but towards the end of the movie the bullet ricochets off his left arm. (00:08:55 - 01:34:45)
Continuity mistake: When Karl Urban is defending the Asgardians, the dust covers on his rifles vary between being open and closed several times. M16 dust covers are sprung loaded - they open on the first shot and have to be manually closed afterwards.
Continuity mistake: When Sammy first offers the drink to Diana (in a close up), Diana takes the mug in her left hand. Just before the camera switches to a long shot, Diana switches the mug to her right hand. In the long shot, Diana still has the mug in her left hand and she sets it on the wall to her left. The camera switches back to a close up and Diana again has the mug in her right hand. When Steve asks her to dance, Diana again sets the mug down on the wall, this time to her right.
Audio problem: Anthony Hopkins is in his car with Cogman, discussing Pangea the super continent over the phone with John Turturro. There are two instances in this scene in which Anthony Hopkins' voice has been dubbed over by a different actor that does not sound like him. Anthony Hopkins first says "That's Pangea. The super continent." The scene then flashes back to the round table and the dubbed voice attempting to sound like Hopkins says "It's the same shape on the round table." The dubbed voice is heard again when he says "Genius", before reverting back to Anthony Hopkins immediately after when he says "Stonehenge."
Factual error: When Xander Cage is chasing Xiang on the dirt bikes, he lets his bike get entirely submerged, which would flood the engine.
Continuity mistake: When the moms are making gingerbread houses the candies on the houses change with each shot.
Factual error: The action takes place around the second half of June (either side of the Glastonbury festival weekend). At the beginning of the film leaving work early evening in time to get home for dinner, in the UK, it wouldn't be dark. Later on, there isn't that much snow in the Alps, especially below the tree line, at that time of year.
Factual error: The Saint steals gold. One gold bar in this movie measures 30cm x10cm at the base and 7 cm high with a 10 degree draft angle. That means about 2.1 liter size and weight of 40 kg for one gold bar. The Saint moves bars with one hand from the briefcase to the backpack, can run and hit etc. The backpack would weigh 240kg and somehow a man runs off with it one one hand. (00:07:00 - 00:11:50)
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