Trivia: In the scene where Anna is outside the gates during "For The First Time in Forever", you can see the backs of Flynn and Rapunzel from "Tangled".
Revealing mistake: When Anna and Hans are dancing in front of the lighthouse, we don't see the shadow of the railing or the ground they're standing on.
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.
Suggested correction: If you watch closely as Elsa is walking backwards she has turned on a slight angle is now walking at an angle to the gap. She then turns round and increases this angle. Not by much but it's enough that she is now walking/running at approx a 40-45 degree angle and she disappears out of shot. We then see her approach a lip of snow (the camera is below Elsa) and form the ice staircase over the gap we originally see.
I see what you mean. Good use of words. They were very scientific.
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.