(at around 18 mins) Ethan Hunt is issued a fake identity card which helps him enter The Kremlin. When he holds it in his hands for the first time, the name given on it says Fedorov. When going through The Kremlin checkpoint, the security guard struggles to find it in the system. He eventually does, but it shows Samokhvalov (read in Russian).
(at around 1h 21 mins) Wistrom and Hunt's car crash happens on an elevated bend of an overpass, yet they are shown on a ground-level open freeway seconds later.
(at around 1h 30 mins) When they are on the outside of the private plane to Mumbai, the windows are round like on a boat. When they are inside the plane, the windows are large and square.
(at around 57 mins) When Hunt and his team are in the Hotel at Burj Khalifa, they see the sandstorm approaching from the front of the building yet when Hunt and Wistrom exit out front (at around 1h 16 mins), the storm hits the building from the back.
When Ethan is broken out of jail, it is the middle of the night and all of the prisoners are asleep. But once Ethan and Bogdan are rescued, they are shown in the van during the day.
In the climax sequence, at the multilevel car park in India, all the cars are left-hand drive but in India cars are right-hand drive, like in Britain.
A magnetic field powerful enough to lift a human being (who was wearing a metal vest) would also wreak havoc in everything electronic nearby, also throwing into the air the very computers the team was trying to access. The average battery pack cannot supply enough power for such a move.
(at around 1h 1 min) When Ethan is escaping the server room by running down the front of the Burj Khalifa he is using a technique called "aussie rappelling". In order to do this the belay device the rope passes through must be positioned at the back of the harness and not on the side as shown in the film. If it was attached this way you would end up going down the building side first and not face first.
It is not physically possible to make a nuclear sub launch a missile within the depicted time frame of 30 seconds, or even a few minutes. That is because it is not physically possible to communicate quickly with submerged submarines. A sub on deterrence patrol is submerged about 200 meters or more where it can only be reached via ELF (Extremely Low Frequency), allowing communication only on the order of a few characters per minute. This is used to transmit a pre-arranged code group to make the sub rise to a much shallower depth where faster means of communication can be utilized. That depth change alone takes tens of minutes.
Ballistic missiles do not fire their rockets after they reach their highest point, hence "Ballistic". All the stages burn out before reaching the highest point of the trajectory ('apogee'). They also are targeted much higher than the ground-level burst apparently intended in the film.
(at around 47 mins) When Kurt Hendricks is talking about nuclear weapons in the TV-interview he is speaking in Swedish to the Russians. The Russians in the background are seen wearing translation headsets.
The camera-projector used to hide the Kremlin hallway is shown gradually changing position depending on the guards eye-line by means of a motorized mechanical arm. After Benji almost gets discovered by accidentally stepping in front of the camera, a tablet is shown displaying a message "render complete", which means the camera was only needed until the rendering takes over, which Ethan confirms by wiping his arm in front of the camera. So the rapid flickering of the projected image when more guards arrive later is totally possible, since the image is now based on a render and not on a mechanical arm moving rapidly.
(At around 74 mins) Benji appears to refer to Sabine by her real name, saying "I can't see Lea, though." In fact he says "I can't see Leonid, though" due to the fact that Wistrom shot Leonid, the guy who authenticated the codes, in the previous scene.
(at around 1h 13 mins) After the exchange of the diamonds for the launch codes, right before Jane Carter catches up with Sabine Moreau, Moreau waits impatiently for the elevator and pushes the button. The whole wall shakes under the pressure of her pushing the button, showing that it is a set. Then Wistrom is in another elevator, which is stopped by Benji, and when he pushes a button to try to start moving again, the whole panel depresses and not just the button itself.
(at around 43 mins) Bullets are shown moving through water at high velocity, endangering Hunt and Brandt. Bullets, however, lose velocity very quickly in a mass of water. Water tanks are often used for ballistics tests for that reason.
(at around 1h 49 mins) The Nuclear Launch Device used by Hendricks has an incomplete Russian keyboard (missing four letters which are normally placed on the right-hand side on QWERTY keyboard buttons with left square bracket, right square bracket, typewriter apostrophe, and slash), and the User Interface is very poorly translated: the title (the inscription above the code) should say "Kod podtverzhdenia", not "Udostoveritelnyj kod" (the word "Udostoveritelnyj" does not exist in Russian at all, although it has some recognizable Russia parts), there is an untranslated word ("dismantled"), and the syntax is awful. (A little earlier in the movie the UI in Engish is shown, yet it of Benji's device, not Hendricks' one.)
Despite having an open window on a multi-story tower, there is very little wind noise and surprisingly none of the character's hair is blowing wildly around. Additionally, given the open window and the height of the building, there should have been a strong wind current rushing through the room. Strong enough to suck people out if they got too close to the edge. However, Ethan, Jane and Brandt all stand at or near the edge of the opening and aren't shown to be affected by that current.
(at around 53 mins) When Ethan is approaching Dubai by road, he is driving on the right-hand side of the road. When they reach the Burj, there is a panoramic view of Dubai and the traffic is seen driving on the left.
When the officer asks to see Ethan's ID, he never asked for Benji's and let him through.
(at around 1h 30 mins) When they are on the outside of the private plane to Mumbai, there is a sound of the jet engine in idle mode. In the last shot of the sequence the sound changes to jet engine throttling. However, we see that the engine blades are standing still and not rotating, hence the engine is not running and cannot produce that sound.
at around 1:37:45 Ethan Hunt audio is "Get us that code!". In video, clearly something else was said.
(at around 53 mins) The reflection of the crew helicopter is visible for a second in the windows as it flies over the Burj Khalifa building.
When Hunt tries to hide at the outside wall of the hospital, a camera shot from below shows a crew person's feet one floor above Hunt.
At 1:33:40 there's a background flash in the airplane.
When the movie moves to Mumbai, India the language depicted is Kannada, but the actual languages predominantly used in Mumbai are Marathi and Hindi.
(at around 14 mins) The initial scene in Budapest is supposed to take place in or near Keleti station but instead it is shot at Central Station in Prague, Czech Republic. This can be validated by the "City Elefant" trains which are in use only in the Greater Prague area.
(at around 1h 35 mins) After the plane lands, they have supposedly arrived in Mumbai. When Ethan Hunt pulls up to Brij Nath's house, you can see both the architecture as well as the environment is Middle-Eastern (most likely Dubai), not Indian.
In the car park scene there is no reason whatsoever for 'Cobalt' to jump to his death with the nuclear launch briefcase. He could simply have thrown the briefcase without committing suicide and achieved the same aim of making it hard for Ethan to get to the case.
Despite climbing on the outside of major hotel across numerous windows, no one notices Ethan Hunt when he makes his ascent or descent.
The US Secretary gets killed by gunfire while meeting Ethan inside his car. Cars for officials like the US Secretary are provided with bullet proof glass. This would have prevented him being shot through the car's windows..
At the Burj Khalifa, Wistrom (Hendricks in disguise) brings Leonard Lisenker to authenticate the nuclear launch codes. The only way he could authentic the code would be if he already knew the codes. If he already knew the codes then there is no reason to buy them in the first place. He might have only been there to verify they were formatted correctly and the paper work looked right, but then the scrambled codes would have still worked.
The only reason the team enters The Kremlin is to find the identity of Cobalt. However, later on, when they identify Cobalt as Kurt Hendricks from Ethan's drawing in the IMF Secretary's car, the Secretary immediately hands Ethan a data file on Hendricks (which Ethan shows to the rest of the team in the railroad car later). If they already know Cobalt's identity, there is no reason to send the team into The Kremlin in the first place. Actually, the reason given for their invasion of The Kremlin when Ethan accepts the mission is that they need to get to Cobalt's file before he can destroy it, not to find out his identity.
Ethan climbs 11 floors of the Burj Khalifa from the outside to break into the server-room which is located on the 130th floor. The IMF team could have just gone to the 131st floor by elevator, broken into a hotel room above the server-room using the laser cutter and then suspended Ethan from a rope to the floor below.
(at around 1h 45 mins) When Ethan Hunt asks Benji Dunn to "pinpoint Hendricks's location", Benji says "Hendricks is signaling from a state-run TV station". However, earlier we saw Hendricks had entered the "Sun TV Network" station which is a private Television network.
As the IMF team visits the party of the rich Indian guy, they communicate to each other by codes names based on planets.. As soon as tension goes up they all give up the aliases and call each other by their normal names.