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.
Continuity mistake: In the shot where Elsa creates the ice wall to push the Duke's bodyguard off the castle her hair is resting on her left shoulder. In the next shot it is flat on her back.
Other mistake: When Anna's horse gets scared and runs off, Anna falls into a stream and gets soaked. Trouble is, everything else in the kingdom is frozen solid - the sea, waterfalls, etc. - there's no way that stream would still be liquid.
Continuity mistake: In Elsa's big number "Let it Go" she pulls her hair down. Her braid goes from being on the left side of her head to being in the center/right.
Continuity mistake: When Anna enters the trading post there is a target next to the door that is facing the same direction as her, but moments later the target is facing Oaken's counter without being touched.
Continuity mistake: When Anna enters the ice palace and slips, she's well short of the staircase. We cut to a front shot and she's suddenly right at the foot of the stairs.
Revealing mistake: Despite all the characters being caught in a blizzard at the end, the snow does not settle on any of the characters or clothing.
Continuity mistake: When Olaf is comforting Anna next to the fireplace, he walks next to a window, pulls off an icicle, and bites the sharp end off and spits it on the floor. In a few shots, the ice pieces are not on the floor, and could not have melted in this time.
Continuity mistake: When Anna blocks Hans from hitting Elsa with his sword, Hans flies backwards. If you look at the spot where Hans should be, he is not there.
Continuity mistake: Just before the end Olaf gets his own personal fluff (a snow cloud). In the scene on the ice in the courtyard following that, the snow cloud is not there.
Suggested correction: It's above him only when it's warm around and he is in danger of melting, but not when it's cold, and it was definitely cold in that skating scene.
Continuity mistake: After Marshmallow knocks the guards into the snow bank, the one on the left has nothing by his hand. We cut away, cut back, and there's suddenly a crossbow bolt under his hand which he grabs before giving chase.
Continuity mistake: Kristoff asks Anna "didn't your parents ever warn you about strangers?" and she edges over in the sled. Shortly afterwards she's suddenly back where she was.
Continuity mistake: After Anna and Hans leave the ballroom, they sit and chat on the balcony. Starting their duet, they wear shoes and boots. Then in the next scene in the hallway they're sliding on their socks and the shoes are gone. As the guard enters the door they exit the the other one. Now as the scene changes to where they jump on the wall, they are wearing their shoes and boots again.
Continuity mistake: When Anna is asking Elsa what is she afraid of, no one is surrounding Anna, but after Elsa unleashes her powers, Hans, the Duke and his men suddenly appear out of nowhere next to her.