Continuity mistake: When Moreau is brought to the room and sat on the chair, her hair swaps from messy to brushed between shots.
Factual error: After the IMF crew rescue Ethan Hunt from the Russian prison, they stop and Ethan Hunt walks up to a payphone. The information on the telephone is in Russian, but worded incorrectly.
Continuity mistake: When Ethan is climbing Burj Khalifa, the sandstorm is approaching from the north. When he exits the building he runs to the north, and the sandstorm is now approaching from the south.
Factual error: When the four main characters get together at the end of the movie and meet Luther, it is said to be in Seattle. Benji says all the people around them were almost vaporized. The nuke landed in San Francisco and if it had detonated, it wouldn't have affected Seattle so drastically.
Other mistake: When Ethan drives a car off the edge of the parking ramp the car falls 100 meters to the bottom pointing nose down the whole way and hitting nose first allowing Ethan to be saved by its air bag. The car's angular momentum makes this impossible - the car would have tumbled back over front.
Continuity mistake: When Ethan disguised as a Russian officer passes the security scan at the Kremlin, he goes without the controller giving him back his fake ID card. In the next shot showing him, Ethan puts it back in his pocket.
Continuity mistake: This is at the fancy car park in India. Hendrick has just jumped off the platform. The briefcase as well as his body move in subsequent shots. Note the lines in the concrete floor.
Other mistake: During the car chase scene in Dubai, Ethan pushes the clutch several times (visible in the leg-room shots). The car, however, has an automatic transmission.
Continuity mistake: In the prison break scene, when Benji opens the second prison cell, the computer shows that he is opening the second cell, but the third cell actually opens.
Answer: He considers Hunt to be a friend, so did what he asked. In addition, by carrying out the deal he has ingratiated himself with Sidorov as well.