Continuity mistake: Outside the trading post, there's no evidence of wind or storms. When both Anna and Kristoff enter, we hear wind blowing, and it's even strong enough to slam the door shut both times.
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.
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: 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.
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: 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