Goofs

Continuity: In the cargo car when Ethan pulls off the mask, his collar is too big for him. The next time we see him it is just the right size.

Continuity: On the train when Max gets the disc from under her seat it is a floppy but when Kittrick asks her for the disc she gives him a CD.

Factual errors: The London-Paris passenger train via the Channel Tunnel is the Eurostar, not the TGV.

Factual errors: When in the tunnel, the Eurostar uses an overhead power cable system; the TGV uses one at all times. No such power cable, which would have made the helicopter interactions impossible, is ever shown.

Errors in geography: The Channel Tunnel has separate single-track tunnels for the two directions of travel.

Continuity: Ethan reaches out and catches a drop of sweat falling from his head while two inches from the floor in the CIA Terminal Room. There is not enough distance between him and the floor for his hand to stop the sweat the way it is shown.

Continuity: Krieger throws a disk in the trash really hard and you can see a piece break off. When Ethan recovers it, it is good as new.

Continuity: Ethan has blood on his hands after finding Sarah and Golitsyn dead, then wipes them off in the phone box while talking to Kettridge. When he throws the chewing gum bomb at the fish tank his hands are clean but when he arrives at the hotel he proceeds to wash blood off them.

Plot holes: When Hunt falls in the computer room, the air pressure generated ahead of his body by the fall would set off the floor alarm if it were anywhere as sensitive as shown.

Errors in geography: When Ethan makes the phone call from Liverpool Street Station the phone number being traced is a Knightsbridge number and not a Liverpool Street number.

Factual errors: Trains run on the left track, both in Great Britain and in France.

Continuity: At CIA headquarters, the fire alarms in three sections are tripped. Then Luther hacks into the alarm system to trip the alarm in Section 21. Later in the Situation Room, the alarm is displayed in a corner of the wall display, but Section 21 isn’t lit up.

Audio/visual unsynchronized: The sound effects used for the helicopter is not of the NOTAR which is the one shown.

Revealing mistakes: In the opening scene, when Ethan gives Claire the injection, you can see that the needle is rounded and not sharp.

Errors in geography: Onboard the Eurostar/TGV, Max is reading the US edition of the Financial Times, as indicated by the American flag in the upper corner. That edition would not be for sale in London or Paris.

Continuity: Claire places the tracker on the NOC list’s technician near the top of his left shoulder. When we see him in the bathroom in the overhead shot, the grey square has dropped to his lower back on the left side, closer to the center. It is visible when he reaches to clean the sink.

Revealing mistakes: In Prague, Ethan walks by the car twice when Claire sees him.

Continuity: After obtaining the NOC list, Ethan Hunt sends a meeting request to Max at the address Job 315. The original Usenet group and email was Job 314.

Errors made by characters (possibly deliberate errors by the filmmakers): When Ethan is quoting the Bible to Max, he says “palaces” instead of places as shown in the Bible he is reading.