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.
Continuity mistake: When Anna visits Elsa in the ice palace Olaf comes in and is on the second to bottom step, with Anna, explaining himself - after Elsa goes upstairs the shot down the stairs has no Olaf, just Anna. (00:55:35)
Chosen answer: They don't restrict her powers, as made obvious by the snow and ice in her room when she's locked in it. They just hide the obvious effects on her hands to try and keep her from thinking about it.
Greg Dwyer