In the Paris scenes, the number plates (starting with BB) on most of the modern luxury vehicles (BMW, Range Rover, etc.) are obviously fake because the current French license plate system has used sequential letters which start with AA since 2009, and has almost reached FA in 2018. Cars with BB... license plates are at least 8 years old.
The BMW motorbikes in the motorbike chase scene have 2 cylinder boxer engines, but they sound like inline 4 cylinder engines. Also, Ilsa's motorbike later on (in the chase where Ethan drives a BMW car) which has a 2 cylinder inline engine, it has the same 4 cylinder engine sound as the other bikes from earlier on in the movie.
In the final scene where Ethan has the detonator component in his mouth and then pulls himself to the top of the cliff he is very clearly clean shaven as the helicopter rescues him. The very next scene he has facial hair that would take several days to grow in when his ex wife is taking to him. If he had been unconscious that long why wouldn't they have at least moved him to hospital?
In the car-bike chase, directly after the car jumps from the stairs , they pass a stop sign and then the biker turns right into arches. As she is turning there are tables and chairs to her left which are empty. But when she turns into the arches behind her the chairs are visible and there are people sitting on them.
During the Paris van chase the hero's van drives down a narrow road finally jamming itself between the buildings. Clearly seen on the right hand building is the top of the wood used to construct the fake walls to protect the real stonework.
The concept of detonating nuclear bombs near a glacier in Kashmir is misconceived. Firstly, we are told that this would affect China's water supply. The main river in the region, the Indus, begins on the Tibetan plateau and flows into Kashmir. Radioactive contamination would not flow upstream into China. Secondly, the contaminated water would only represent a fraction of that flowing into the Indus River. The Shyok River could be dammed to prevent contamination of the Indus River if necessary. Thirdly, it's quite likely that bombing the area would have very little impact, so it's unlikely to be chosen as a target.
In the final helicopter chase scene, Tom Cruise's and Henry Cavill's characters depart from a village in Kashmir and in a few minutes end up in Norwegian fjords (more than 5000 km away), clinging to the cliff of Preikestolen (Pulpit Rock), the iconic mountain plateau in Norway. The cliff is one of the country's most popular tourist attractions and has been named one of the world's most spectacular viewpoints by Lonely Planet, therefore can be easily recognized.
Early when Hunt and Hunley meet at Ramstein Air Base, the layout is completely wrong and obviously not Ramstein. Built in the late 1940s, RAB only has one hangar, which is considerably smaller and less modern-looking than the hangars seen in the film. It is actually a station called Royal Air Force Brize Norton in Oxfordshire, England.
At about 49 minutes into the movie, the helicopter carrying Lane is first seen flying eastward, above the Eiffel tower (west of Paris) then above the Tuileries garden, but in the next shot it is flying westward above Notre-Dame, when it should have kept eastbound to reach Bercy.
While the specifications for the bomb were being revealed, an explosive yield of 5 megatons was mentioned. This would be impossible since a plutonium core alone would only be capable of a fission reaction measured in kilotons of tnt . A secondary or even third stage involving a fusion reaction would be necessary to achieve an explosive yield in the multi-megaton range. This would require fuels such as lithium-6 deuteride and tritium and a much more complex design that what was in the movie.
Plutonium is very heavy, so assuming each ball of plutonium is 4" in diameter, then each ball would weight about 25 lbs. Given that weight, it would be difficult to pick up one ball as easily as the IM team members do at the end, or for the henchman to so easily move the suitcase holding all three balls.
Several people are tracked with microwave transmitters that are injected into their bodies. The problem is that microwaves (above 300 MHz) can not penetrate human bodies because of their water content. Implantable RFID tags for the identification of animals, for example, use much lower frequencies (120 to 150 kHz).
In the final fight the helicopter was being held on by a nylon rope to a hook on the rock, perhaps enough to hold the 2000# ACFT wreck. Yet, when Hunt is climbing the rope, there is enough slack for him to use the wrap in the rope around his leg, to climb the line, When the ACFG slips and falls with his leg wrapped around the rope, there would be enough power to sever his leg.
The German license plate of Ethan Hunt's BMW at 'Ramstein' air base starts with a 3 digit number (8xx?). German number plates start with one to three letters (representing the city/county), followed by one or two letters and a one to four digit number.
As the team arrive in London the van they use does indeed look wrong for a UK plate but the first letters are spaced differently. UK plates usually have 2 letters,2 numbers followed by a space and a final 3 letters for example in the movie the plate started for example
BT 12ABC when it should have read BT12 ABC.
When Hunt and Walker put on pressure suits with helmets just before they jump off the plane, the helmets are illuminated from the inside. Nobody would actually do this, because the glare from the light inside the helmet would completely destroy visibility for the wearer.
When the bathroom fight is over, you can see both of them stepping in the blood puddle. That would've left bloody footprints all over the white tiles on the bathroom floor. Yet when they walk around there is no footprints mark anywhere.
It is incorrectly regarded as a goof that the 15-minute countdown lasts 25 minutes. There are multiple story threads in different locations. If we spend 3 minutes with Ethan in a helicopter and then 3 with Benji and Ilsa on the ground, that doesn't necessarily mean that 6 minutes have passed; we may be seeing what different characters did during that same 3-minute period. This is non-linear editing.