Continuity mistake: The Chechen brothers approach Nikolai in the sauna. Viggo Mortensen has a towel draped across his back, with an irregular profile, covering the right shoulder more than the left. After a brief cut on the hitman preparing his knife, there's a close-up of Viggo, with the towel neatly arranged and properly balanced. (01:17:45)
Continuity mistake: Nikolai gets hurt for the first time (slice across the chest, shown in a close-up) by one of the hitmen. He punches the aggressor in the face, who bounces against the wall. His hand is in plain view and there's no weapon. Next shot, he's brandishing the knife, and drops it only a moment later. (01:17:55)
Continuity mistake: The bigger Chechen assassin punches Nikolai after the first slice across the chest. When Viggo is rolling on the floor and ends up on all fours close to the wall, his chest is quite clean, but when the guy angrily walks up to him, his chest is a bloody mess just before getting kicked. (01:18:05)
Continuity mistake: After some fighting on the floor, Nikolai manages to put a knife in the chest of one of the sauna killers, and is fighting with the other. They get close to two poor dudes who are minding their own business; in the first shot you see the younger of the two completely stepping out of the way, a good couple meters away from the action. In the next one though, Viggo, the aggressor and those 2 are practically in a single line. (01:18:50)
Continuity mistake: Anna sits by Nikolai at the hospital, and after a while, he turns towards her as she moves her hands to her thighs. The next shot though has rather spotty continuity; Anna's hands are turned differently, the eye contact with Nikolai is lost, and the heart monitor from 47-48 has now a mostly steady 55 pulses. (01:21:45)
Continuity mistake: Looking at the security monitor as he talks to the young Maria, Kiril has a balloon between his hands that is balanced differently between shots. (01:26:40)
Continuity mistake: In the finale, once Nikolai delivers the line about being king, the baby cries. From that point on, the side views come from takes filmed while the baby was sleeping and therefore is quiet and still, while shots from a different angle have Christine moving. (01:32:35)
Continuity mistake: During the kiss and farewell with Nikolai, Naomi Watts' hair is all agitated by the wind in every shot from one particular angle (camera behind his shoulder), and goes back to being unperturbed at the cut. (01:32:55)
Continuity mistake: Naomi Watts holds the baby to her chest while Viggo Mortensen walks away; she is supporting her with her right hand behind her head, which becomes the left hand in the faraway shot. In the same shot, Kiril is jumping around, but is leaning against the wall at the following cut. (01:33:30)
Continuity mistake: When Nikolai and Semyon are drinking vodka during the diary exchange, Semyon empties his glass, but when he puts it back on the table it is full.
Continuity mistake: When Anna handles the diary of Tatiana over to Nikolai at the fast food restaurant, Nikolai's right hand does not have the big tattoo.
Suggested correction: I don't think I can confirm this mistake. The hand that takes the diary in close-up is the left one, and when he uses the right hand, the tattoo is there. It's a faded tat to begin with, so if the streaming quality when you watched it was not optimal, it may be a detail easy to miss or that blurs out with compression noise. But it is there.