Factual error: Towards the end of the film, Solomon is trapped in a small Plexiglas box and fires his gun into the bulletproof sides numerous times, but the bullets don't ricochet or get embedded in the glass.
Revealing mistake: When Benji imagines putting on a mask of an agent he plans to impersonate, when the camera pans around to first show the mirror, the mirror Benji's hands are further up on his face than the reflection, and the mirror Benji's hands move down his face slightly before the reflection starts to move them. Also, the mole that Ethan has on his left cheek isn't reversed in the mirror image. The "mirror" was actually a hole in the wall between two identical sets (one mirrored), with Simon Pegg and a Tom Cruise double in the foreground, and the mask actor and Tom Cruise in the background "mirror" set. (00:57:20)
Factual error: When the gas is turned on for the box, the red handle was moved to a right angle to the pipe which is standard for the off position.
Continuity mistake: When Ethan and the girl are sliding down the rope at the opera, in one shot, as it should be, her dress is up around her neck - that is all we see - and in another shot, the dress is down around her ankles, which it shouldn't be.
Continuity mistake: During the bike chase scene, Ethan chases the last rider who is trying to shoot IIsa. He follows a right bend to catch and get in the inside of this rider. Ethan then knocks him from the inside of the bend. As he is on the inside of the bend, he would be knocking the rider to the left. However, in the next shot Ethan has knocked him off on a straight road with the bike and biker now falling to the right, which would be impossible from the previous shot, with both rider and bike falling towards an embankment. In last segment the scene changes back to Ethan exiting the bend with the rider's bike travelling now in the opposite direction along the ground towards the edge of the road, before exploding when hitting the barrier. (01:16:00 - 01:17:00)
Plot hole: Before the IMF team can exchange the yellow cards for the access control, they first need to know the data format/file type in which the access rights (retina, gait, fingerprints...) are stored. Otherwise, the computer will not recognize the data on the card, and display an error to the maintenance personnel. In order to figure this out, they would need to steal first some of these yellow cards and analyze the data on them, before they can fake a card which will be accepted by the computer.
Factual error: They are meant to be taking off from Belarus in the opening scene. However when they fly over the roads the traffic is driving on the left hand side of the road.