How is she the ghost?
I'm going to talk a little about Alfred Hitchcock's bomb situation, and how it relates to this ending, and why I hate it so much.
The ending of Another is a surprise. There is no way the audience could have guessed Reiko was the ghost, apart from one throwaway line by her father, who is mourning the loss of her sister, and says something along the lines of "I'm sorry Ritsuko, I'm sorry Reiko" which doesn't really imply that Reiko has died, nor do we ever hear anything like it again. So we just assume that the father is mourning the loss of the daughter which is gone, and is apologising to the daughter he has left because he could save her sister.
The ending of Another would have made a much better ending if we take the suspense approach from Hitchcock. Mei knew all along that Reiko was the ghost, she even saw Reiko get killed. Why didn't she say this to anyone? Even if they didn't know that killing the ghost would have stopped the calamity, it would have made sense for her to speak up and say "the assistant teacher is the ghost", even if just to one other person, that way they would have known, and we the audience would have known. And from that moment on, every interaction we see with Reiko and another student, would have made for a much more suspenseful experience.
To go back to Hitchcock's original situation. If everyone had sat at the table, and there was a bag below the table that no one noticed, but was obvious for the audience to see. The ending is still a surprise, as no one knew that the bag had a bomb in it. However, there was no bag equivalent in Another. The bomb went off, and a small explanation happened afterwards, nothing really to make you feel the 11 episodes prior really meant anything to the story's resolution.