Matthew's sister fires a shot at Diana cocks the hammer and a few seconds later fires a second shot. That would be impossible for the type of guns used in that era. The gun she is using a single barrel muzzle loader which means she would have to reload it by placing a gun ball in the barrel, pouring in black powder, stuffing a small cotton square plug in the barrel, then use the rod under the barrel to tamp everything down. Only then could she fire a second shot.
When Matthew's sister appears in the cave behind Diana, she has her right arm slung over Diana. Diana, in turn, is choking. However, Louisa's arm is not around her neck and therefore couldn't be choking Diana.
When Matthew tells Queen Elizabeth that in 500 years, everyone will know her name, Queen Elizabeth I, it makes little sense in context. Queen Elizabeth didn't go by Elizabeth I. Instead, she would have been called Queen Elizabeth. Her name, as Matthew says, is known to us 500 years later, which would have sufficed without adding the first to it.