Continuity mistake: Besides the fact that during the final action sequence it is impossible for two trains to occupy the same tunnel, how is it that the blades of the helicopter attached to the first train don't strike the second? Tight fit.
Continuity mistake: In the scene where Ethan is in the NOC list room Krieger starts to drop him and Ethan is hanging there for a little while. Suddenly some sweat starts to drip down his glasses and he catches the drop with his hand. If you look at how close he is to the floor this move would be impossible.
Continuity mistake: The train is electric, supplied by overhead cables, which do not appear to be present at any time. If it was a Eurostar then it could use 3rd rail pick-up but it wouldn't be going so fast, but that's academic; its not a Eurostar and no 3rd rail is visible either.
Continuity mistake: When Ethan is being lowered into the room with the NOC List, he has the digital temperature gauge. As Ethan is going down, the gage is right side up so you can read it normally. However, Ethan is upside down, and therefore so are the camera glasses he is wearing. Now when we see the computer screen that Ving Rhames is using, the gauge is right side up there, but it should actually be upside down.
Continuity mistake: At the end of the film, Ethan drops his mask. His hair looks flat and wet. At the next shot it's dry and up. (01:34:20)
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."
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)
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)