Continuity mistake: When Anna, Kristoff and Olaf get thrown by Marshmallow, Anna does not have her hat on when they are sliding, yet her hat is back on in the next shot.
Continuity mistake: When Anna and Kristoff fall off the cliff after being chased, they are still tied by the rope. When they land the rope is gone.
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: Anna walks a few feet to put Olaf's head back the right way on his body. After she does this, she is back to the position she started in and Olaf has moved between Anna and Kristoff.
Other mistake: Anna is shown from the front as she ascends an ice staircase inside Elsa's ice castle. There are giant ice pillars to Anna's right and left. They should reflect the side of her face, but instead the reflections show her face from the front.
Revealing mistake: When Anna and Hans are dancing in the spotlight, their silhouettes should be casting shadows as well, but aren't.
Continuity mistake: In the scene where Kristoff and Anna are riding on the sled, in the first shot of them in the sled, Anna's hair is behind her, flowing in the wind. In the next shot, her hair is in front of her, resting on her chest.
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 Anna is singing "For The First Time In Forever", at one point she is walking along the railing of a bridge. As she is doing so, she passes a guy in a hat, holding his daughter. In the next shot, the guy and daughter completely disappear.
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.