Continuity mistake: In "Let it Go", after Elsa releases her cloak, an overhead shot shows she's about 30 feet short of a gap, walking forwards, on a flat expanse of snow. She then keeps moving towards it while singing in closeup (which would have taken her right up to the edge). She then runs forwards in a wide shot, but instead of falling off the edge she should be right next to, she runs up over a hill that appears from nowhere, before she creates the steps to bridge the gap.
Continuity mistake: During the song "For The First Time in Forever", Anna runs into the gallery and a painting of a woman on a swing is seen to the right of the door. Later in the scene she is seen leaping off a teal-colored seat to make the same pose as the woman. This is impossible since we never see her cross in front of the door to get to this painting, which means she would have had to have jumped very far to get to the swing painting.
Continuity mistake: When Sven and Kristoff are leaving Arendell, Sven looks back wistfully to the city, but it's not in the distance where it should be. We can also see their footprints left clearly in the snow - it's not snowing much. When Kristoff then runs back, Arendell has suddenly reappeared, and there's no sign of their footprints. It also takes him far longer to get back to the city than it took him to leave.