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.
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: 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)
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.