Continuity mistake: In the scene where Red is trying to escape from the dynamite-filled cable car, we see the burning fuse as she climbs out of the car. A moment later we see her climbing up the outside of the car, and the fuse has disappeared. Later, when Grandma causes the car to fall into the river in the nick of time, the fuse is just burning through the window space.
Continuity mistake: When the wolf and sheep are talking, look at the right side of the wolf. You can see a dandelion. In the next shot it's gone.
Audio problem: In the scene when Grandma is at the tournament (but not yet skiing), in the cuts when the band isn't visible, if you listen closely, the lead singer isn't singing. (01:05:05)