Continuity mistake: During the end bike chase scene, Ethan Hunt has just used his mirror to fire his Beretta at Sean Ambrose, he then re-holsters the weapon and swerves round two cars. If you play the movie slowly you can see that after he re-holsters the gun it is still in his left hand while he is holding onto the handlebars. It's a quick shot so you have to look carefully.
Continuity mistake: At the rock climbing sequence, after he slips and is hanging by one hand starts staring at the landscape, in the wide shots, the sun is directly behind him, but in the closeup shots, he is in the shadow. (00:07:45)
Continuity mistake: During the motorcycle scene near the end of the movie there is a shot of Cruise from the front. You can clearly see an earring on his left ear. A second later it's gone.