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.
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: As Elsa sings "Let It Go" she pulls her hair into a long braid going down her back. She pulls it with her left hand from behind her to in front, but the end doesn't flip over her shoulder, she just pulls it straight through to the other side without going over the top. (00:34:10)
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. (00:15:05)
Continuity mistake: Just after Anna gets unfrozen and Elsa realizes love is the key to end the winter, Elsa starts to unfreeze everything. She is doing this in the middle of the lake. The ship they are standing on a shot later is not there when she starts unfreezing things. (01:28:00)
Other mistake: When Elsa is about to get shot, Hans, from where he was, couldn't have possibly got to the guard in time.
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.
Continuity mistake: Towards the end of the scene where Hans is about to kill Elsa, the camera pans to a wide view of Anna standing on the ice on her own, Elsa and Hans are nowhere in view, yet a few seconds later as Hans brings his sword down on Elsa, Anna appears and parries the blow. In her fragile and barely able to walk state, there is no way Anna could have covered this distance in the time given.
Continuity mistake: The snow covering the mountain varies between shots of the first sighting of the ice castle and when Sven attempts to climb the stairs.
Continuity mistake: When Anna, Sven, and Kristoff are being chased by wolves and Kristoff is hanging onto the sled by only a rope, Anna sets fire to his sleeping bag with a torch and throws the torch onto the ground. In the next shot, the torch is nowhere to be seen. Handy, because if it hadn't disappeared the sled would have caught on fire too.