Plot hole: When Ethan meets the Secretary in the car, he tells him that Hendricks was seen leaving the Kremlin with the nuclear launch device and deduces that he is Cobalt. The Secretary then gives Ethan the flash drive containing his mission, which Ethan reads on the train. Ethan then tells the rest of the team that - according to the mission - IMF believes that Hendricks is Cobalt and was seen leaving the Kremlin with the launch device - hence why he needs to buy the launch codes from Moreau. How could IMF have known about this information to put it on the drive, given that Ethan just told the Secretary in the car?
Factual error: When Tom Cruise chases the villain in a parking lot in Mumbai, the "Parking" sign is written in Kannada (the scene was shot in the Sun Network station at Bangalore). Regional signs in Mumbai are in Hindi or Marathi (the state language of Maharashtra, of which Mumbai is the capital).
Continuity mistake: Early in the film, Ethan is talking with Jane in the back of the van after they have dropped off the Russian. There is a silver flexible arm lamp hanging down that is visible when the camera is on Jane, when the camera cuts to Ethan and back to Jane it is no longer visible. A few camera shots later and it has reappeared in the original location.
Continuity mistake: After the sandstorm ends, there's a shot showing Ethan's back and the sand moves away. Ethan's shadow is behind him, meaning that the sun is in front of him, butwhen the shot changes to view his front, the shadow is in front of him, meaning that the sun is now behind him.
Factual error: In the scene where Tom Cruise enters the server room and plugs his thumb drive into the server, it is a Dell power edge 2650 which was released around 5/6/2002 and stopped shipping around 8/13/2004. The building was opened in 2009 - it's beyond belief an ultra modern building would be run using a cluster of out of date, out of warranty, underpowered computers.