Continuity mistake: The doctor tells June that she needs stitches. He walks away offscreen and his reflection shows that he immediately kneels down. From a different angle, he is standing, walking several meters ahead, and he doesn't kneel after several seconds later.
Continuity mistake: When Offred watches her daughter asleep the girl's head is turned to the left, then for a brief shot it swaps to being turned to the right. Then back to the left for the rest of the scene.