Continuity mistake: Ethan and Grace are in a car chase, trying to get away from Paris. The Fiat Ethan and Grace are driving makes a left turn, and you see a dark blue car parked at the corner. Paris is driving the armored vehicle and makes the same turn, but the dark blue car has disappeared. (01:07:36)
Continuity mistake: During the Venice scenes, Ethan's hair length is always the same, except for scene number 1 where he and the team are on a boat arriving in Venice, and scene number 3 where he and Ilsa are on a balcony. In both these scenes, his hair is very short.
Continuity mistake: When Paris kills the two men on the train and starts walking towards Denlinger, her bangs are on top of her head all messed up. Cut to a face shot of her, and her hair is back to perfect.
Continuity mistake: When Ethan jumps into the back of the van with Benji, the passenger seat is empty. However, once inside, Elsa Faust is present.
Continuity mistake: During Paris and Gabriel's fight in the train, the dead guy behind has his eyes open all the time except for a brief shot where they are closed. A shot later they're open again.
Continuity mistake: When the submarine is hit, the centre is blown into a million pieces. In the next shot, the submarine floats gently to the sea floor untouched. Then it semi-crumbles as it lands.
Continuity mistake: When Grace crashes with the Italian police car, the door is opening up on the top because it was dented. When she puts it in reverse, the door is back in a normal state.
Continuity mistake: On the roof of the train, Hunt is on top of Gabriel, with a blade right next to his neck. Gabriel says "I know what the key opens," and right then the blade is either touching his skin or inches away, depending on the shot.
Continuity mistake: When being arrested after the car chase, Hunt and Grace are told to put on the handcuffs. They have their hands up, and neither is holding the cuffs. Then, fired upon, suddenly they are cuffed to each other. Even if explained as a sleight of hand out of shot, from a plot point of view it makes no sense for either of them to cuff themselves to the other at this point. Hunt is trying to save Grace, which makes it harder to do so, and Grace is trying to escape from him, not anchor herself.
Continuity mistake: In the desert, when Ilsa is shooting with her eye patch on, a strand of hair on her forehead suddenly disappears between shots.
Answer: Maybe they didn't have any guns at that point.