How many arrows does she really have? When standing sideways out of a mountain side and firing arrows at the pursuers, the amount of arrows in the quiver continually change between shots.
The wound on Kate's shoulder has varying degrees of healing throughout the movie - running the gamut from red and raw to healed and scarred over.
In an early voice-over it is stated that when the Earth fell out of orbit, particle accelerators were used to try to reset it. There is no reason why the Earth's orbit - or that of any other planet - should suddenly change, but even accepting this for the sake of the film, particle accelerators would be totally useless to try to correct the situation. They only move particles - sub-atomic particles - and even at speeds close to that of light, their mass is so tiny that they would no effect on the Earth's movements.
@ time: 1:11:17 or there about...a pair of tan boots are visible on a rock ledge, upper right corner of screen.
The sides of the pool are seen in the reflection of the water in the underwater sequences in the beginning.