Plot hole: There is no reason whatsoever for Jim to have brought the bible from the hotel with him. Max says that Job never quotes scripture in his messages, so he has no reason to bring the bible. The only biblical reference is job 3:14, and that is simply a phrase to remember: having the bible with you will not help you remember it in any way.
Factual error: The train is running on the right-hand track, but in the UK and France trains run on the left-hand side.
Factual error: Liverpool Street Station is shown as more or less deserted in the hours of daylight. The only way this could be achieved in real life is by phoning in a bomb threat.
Suggested correction: It's night. After Ethan sees that his parents have been arrested, he walks out in the streets, and it's dark outside. Several shots later the big clock in the station is shown, and you can see that it's about 11pm.
This validates the entry rather than correcting it. If it is 11.00 pm the pubs have just closed and Liverpool Street Station would be heaving. This is true of any mainline station in London - as well as the fast food restaurants associated with them. Any Londoner knows that.
Visible crew/equipment: When Ethan is going down to the security room on a rope you can see a man standing on the floor at the bottom. It's right after he starts to descend.
Revealing mistake: When Ethan uses the magnetic screwdriver to undo the screws holding the grille to the air-vent in the NOC list room, the spindle that is actually turning the screw is visible after it falls out.
Other mistake: The version of the Bible which Jim Phelps supposedly got from the Gideons at the Drake Hotel was a New International Version (NIV). The Gideons International distributes only the King James Version (KJV) or the New King James Version (NKJV).
Continuity mistake: At the end of the movie, when Ethan and Luther are sitting at the pub, just after the cheers/here's to you speech, Luther said "Hey, I'm flavour of the month" and brings his glass up to his lips for a drink. In a split second cut to a wide shot facing Luther his glass is on the table, and there are only two glasses on the table as established in a wide shot where Ethan says, "I'd better go catch my flight."
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.
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.
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.
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 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.
