Continuity mistake: When the girl is about to lower the boy down on the rope to save their dad, she loops the rope through the carribena, but she never actually does it up.
Continuity mistake: The kids are repelling down a steep icy ridge. The polar bear is at the top of the ridge above them. The girl is on her way down, and her brother says something to the bear cub. Before he speaks he is holding onto the rope that his sister is attached to, then they cut to a shot of the bear, then back to the boy and he is now holding an axe, with the rope nowhere to be seen.
Continuity mistake: When the kids are climbing down the icy hill, Sean holds an ice axe that keeps switching hands in different shots.
Continuity mistake: When the kids are climbing down the steep icy hill, Sean falls and hits his head on a rock. When he lies unconscious, his head is right next to the rock, but in the next shot we see of him, he's a few feet away.
Continuity mistake: When Shawn and his Dad are arguing, Shawn puts down his fork in one shot, and in the next shot, he has it back in his hand. In the next shot, it's back on the table and he picks it up again.
Continuity mistake: When the boy slides down the hill on the snow/ice and hits his head, he looses his hat. When they are shown hiking in the woods a couple minutes later, he has it.