Continuity mistake: When Greta is packing her belongings away in a box, objects like rubber bands keep appearing in front of it, without her putting them there. The angle of the box changes as well. (00:44:15)
Continuity mistake: When the Dowager Empress is walking towards the door and says the cinnamon smell is from an oil, her reflection in the mirror exactly matches her movements, including when she turns, when it should show a mirror image. Note the blue sash is on the same side in both. A quick reflection of Anastasia's head just before when she says "I just want to know who I am" has the same problem. After they sit the reflections appears to be right. (01:09:40)
Continuity mistake: When Celine is tied up playing blackjack, the position of the rope holding her varies. We see for example that the number of times the rope crosses her chest goes from three to four and back again.
Revealing mistake: During the opening scene, a few shots after we see the Outworld ninjas falling through the portal and leaping about, there's a shot of several monks fleeing that tilts up towards the (digitally replaced) sky. As it does this, you can see several hard lines about in the sky from where pieces of the digital animated skies were "stitched together." It's easy to miss the first time, but if you know to look for them, they're pretty obvious. You can see similar lines in the sky in several other shots throughout the scene, but it's most noticeable here.