Continuity mistake: The little projector in the Odyssey book only lights off at the end of the briefing video, but in the following frame when Ethan closes the book it's already back inside it. (00:04:50)
Revealing mistake: Fight in the toilet of the Paris nightclub: the presumed Lark rips out the sink's drain and begins assaulting Tom Cruise with it; Walker intervenes holding him, but the nimble Asian does a flip and brutally tosses him to the ground. As Henry Cavill is bent over before being snapped to the floor, on his back, you can definitely see a protective pad through the jacket. (00:31:52)
Continuity mistake: During the rescue of the White Widow, she stains her clothes with blood, from the left bust to the side, in the next scene, the stain is no longer on her bust, only on the abdomen and very small. (00:40:05 - 00:40:28)
Other mistake: When Solomon Lane is being extracted out of the sunken truck there are two divers breaking in. However just a moment later only Benji surfaces with the prisoner while Luther is on the lookout on the rib. (00:55:11 - 00:55:36)
Continuity mistake: In the bike chase, Ethan has side mirrors in all but one scene where he is surrounded by police coming from all corners. The bike's mirrors are missing then. (00:59:10)
Continuity mistake: When Benji is sitting back to back with Soloman Lane to duplicate Lane's face, his jacket is green, then they cut to face Luther asking whether Benji is OK, when they cut back, Benji's jacket is the same brownish color of Lane's jacket. Later, Benji wears the green hued jacket again when talking to Luther and Elsa. (01:23:30)
Deliberate mistake: When Walker leaves the tunnels in London and Hunt follows him, they both start their way to the Tate Modern Museum at Queens Head Passage / Paternoster Row. While Hunt is being chased and cannot choose his route, besides not knowing about Walker's destination, Walker deliberately takes a detour to Blackfriars Station and the bridge, even though he could just have walked a direct line from St. Paul's Cathedral towards Tate Modern using Millennium Bridge to directly cross to the museum and his getaway. The whole chase sequence would be obsolete. (01:31:58 - 01:36:56)
Continuity mistake: As Ethan climbs out of the hatch (on top of the Tate Modern) he leaves it open and runs to catch the helicopter opposite him. However, he misses it and is left alone on top of the Tate facing the helicopter. As the camera pans around the hatch is now to the right of him and closed. (01:51:10 - 01:51:35)
Factual error: After a helicopter warning signal says pull up, Ethan pulls back on the cyclic control. All that would do is slow the helicopter by changing the blade angles. He should have pulled up on the collective between the seats. (01:56:15)
Continuity mistake: When Ethan is thrown from the helicopter, he lands with a straight black strap attached to his left wrist. When he comes to a few seconds later, the strap is now doubled up and he's gripping it, it's not attached to him. (02:03:30 - 02:04:30)
Continuity mistake: During the getaway in the 4-door olive-green BMW, in one shot, the driver's headrest is bent forward; in the next shot, it is shown back in the straight-up position.
Other mistake: When Benji takes off the Wolf Blitzer mask, he continues to talk with the anchorman's voice until he takes off the voice altering tape too, but when Walker realises that he is not talking to Solomon Lane and proceeds to rip off the mask, Benji talks with his own voice without taking off the tape.
Continuity mistake: The scenes in London show the Thames river at low tide in some shots and at high tide in others.
Factual error: The three plutonium spheres appear to be about six inches (15 cm) in diameter. At that size, and at 19.3 grams per cubic centimeter, they would weigh about 102 kilos (220 pounds), far too heavy to be carried around so easily.
Factual error: When Ethan enters Ramstein Airbase, he drives a BMW with a German license plate that can't possibly exist. The only German license plates starting with digits are for official diplomats. There is none starting with 881, the highest is 205 anyway. Another mistake is that even if it was a car of a diplomat, the license plate would have additional lettering next to the country letter D (for Deutschland), in Germany that would be CC or CD.
Factual error: The white van in London has a registration mark BT 34873K that would never be possible in the UK. Yes they've just arrived from mainland Europe, but no country in Europe uses that format on registrations, combined with the style, type and display of the actual plate.
Continuity mistake: During the first chase in Paris, the streets are dry, then suddenly wet.
Plot hole: On the plane they are told they have 2 mins to suit up, then once suited up they have a further 10 seconds before the rear door opens. 2 minutes is not enough time to put the equipment on to do the halo jump.
Plot hole: Ilsa had no idea where the BMW was going - she was already on the bridge and in position when we see it turn left into the street, it could've easily have gone straight on.
Revealing mistake: When the toilet fight is over, there's a pool of blood on the floor where Ethan steps on. However, he then moves around the place but leaves no footprints, revealing the blood is CGI.
Answer: They are in France. The French word for police is "police."