Continuity mistake: On the subway while John and Cassian eyeball each other, from the front there's no-one in front of Cassian, just a guy in a hat off to the side. But from the back, another man appears between them.
Suggested correction: You can see the edge of that guy cut off on the edge of the shot he is there, that grey hair and that same jacket.
Continuity mistake: When John gets out of his car at the very start, he is on a zebra crossing. When he gets back in, the car is no longer on the crossing. It's hard to tell, but the car has moved. (00:02:00)
Suggested correction: The car is still on a zebra crossing, when John gets back in. Stripes are very obvious.
Continuity mistake: At the beginning while John is talking with Winston at the hotel, the sun changes between shots. (00:28:00)