Continuity mistake: In Red's story, the scene in the forest with the Wolf has little light due to the trees, but in the Wolf's story it is daylight with no shadow by trees.
Continuity mistake: Granny grabs the first-place trophy as she passes the finish line. However, in the next shot, the trophy is gone.
Continuity mistake: When Granny first skis up to the other skiers, she is holding the skis in each hand. Then, she pulls a big box of snickerdoodles out of nowhere.
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.