Factual error: In the scene of the eurotunnel train the ticket collector is wearing a 70s British Rail uniform This was the national railway company for Great Britain but is now defunct due to privatisation in the 90s.
Suggested correction: At the time of filming, British Rail would still have existed as it was only being dismantled in the mid 90s. However, I think Eurostar would provide their staff with different uniforms.
Plot hole: Accessing the secure room through the duct work would be virtually impossible (pardon the pun). First is this an air supply duct, return air supply duct or an exhaust duct? If it was an air supply or a return air supply duct there would be a squirrel cage fan moving the air. Not the propeller fan you see in the frame. If it was an exhaust air duct again no propeller fan. The size of whatever duct it is for that size of a room is questionable. The room was small yet the duct was large enough for a man to crawl through. The last reason why this would be impossible is where are all the screws that ducts are assembled with? They would definitely stick through the ducts and catch clothing, scratch hands, heads etc.
Factual error: The TGV (and also Eurostar) trains are powered by an overhead power transfer, so an escape from the train with a helicopter would indeed be a Mission Impossible.
Continuity mistake: When Gene is handed the watch in London, the way he holds it changes depending on the angle. (01:25:10)
Continuity mistake: As the firefighters are entering Langley they mention they need to shutdown the air conditioning. The guard states that the aircon is in sector 21 that has no alarm. Luther 'helps' by triggering the alarm in that sector. A while later when Kittridge is talking to his people in the ops room you can see that the alarm is active in the 3 sectors as the guard mentioned but now sector 21 is missing. (00:57:30)
Continuity mistake: In the scene where Jim, Claire and Ethan are in the baggage car of the train Claire takes the money off of Ethan, the money is not folded in any way. However, in the next shot where she passes the money to Jim it is suddenly folded conveniently to fit into Jim's pouch.
Factual error: In the scene in the aquarium restaurant where Kitridge reveals to Ethan that the operation was a mole hunt Ethan uses the chewing gum explosive to smash the glass and make his escape. However, the explosion also causes a man within the aquarium restaurant to go flying through the air and through the window. It is physically impossible for a chemically composed explosive of that size, that is not enclosed, to create enough force to move him in that way, add to the fact that he is seemingly the only person or object (besides the aquarium glass) affected by it, all these combine in making this scene physically impossible.
Plot hole: There is absolutely no way Jim Phelps would have "died" when he got shot even if he was faking it. The first time we see his death he's pointing his gun right at the camera on his glasses which are on his head and not his chest. Later when we see the how he fakes his death he's not pointing the gun at himself anyway so he wouldn't be able to get the angle of the gunshot from his camera's point of view as we saw the first time.
Plot hole: In the famous raid on the computer room raid, where Hunt is lowered from the ceiling, we see a close up of the screws to the vent being undone and caught in a holder so they don't fall on the floor. But the screws cannot be put back in their holes and done up once the vent is closed, and there is not enough time for Hunt to be pulled back up and the vent closed and screws replaced when the operator returns to the room, as Hunt was pulled back up with seconds to spare.
Suggested correction: They would not have to use screws to reattach it. They could use tape, glue, or magnets.
Continuity mistake: When the "firemen" (Ethan Hunt, Claire Phelps, Luther Stickell and Franz Krieger) leave Langley, Claire is in a red coat and red dress. As we see all four drive off in a fire truck, Claire is in a fireman's costume. Firstly, when did she have the time to change and secondly, why change? (01:08:00 - 01:10:00)
Visible crew/equipment: At the end of the film, when the news about the train and helicopter accident plays on the TV, as the camera pulls out, the camera's reflection is visible in the blue window shutter. (01:44:08)
Revealing mistake: When we see a close-up of a knife being pulled out of a man's stomach, it's obviously a prop knife where the blade goes into the handle, as we can see the end of the blade while it's being pulled out. (01:19:50)
Plot hole: At the end of the tunnel, the helicopter has been attached to the train; Phelps knows it, the pilot knows it, and yet Phelps still climbs across to the helicopter like he's trying to escape, but there's nowhere to go. He's deliberately climbing into a potentially lethal situation he can't get out of for no reason except it makes it convenient to kill two bad guys with one explosion.
Suggested correction: Phelps detached the cable before he jumped to the helicopter. The problem was Krieger tried to kill Hunt first, before trying to escape.
Continuity mistake: During the Job 3:14 scene, Ethan places the Bible parallel to the laptop and the gun. In the close-up angle it always appears that way, but in wider angles the laptop is slightly slanted. (00:34:15)
Continuity mistake: When Claire finds Ethan disguised as Jim, he has his normal hands. However, in all previous scenes of him in disguise, he has fake hands as well, that are wrinkled like Jim's.
Continuity mistake: At the end, Ethan is drinking a pint and leaves a little left in the glass. This little bit of drink then vanishes is subsequent shots. (01:40:30)