What happened?
I'm discussing the end of the movie here, so if you haven't seen it, don't read on...
For most of the movie I was sure I had the twist ending figured out in advance. I thought for sure the old man and the murderer were the same guy, and that the old man had killed the child decades before while working at the orphanage, and was simply tormented by the memory of what he had done (or by an actual ghost of the girl). Which would have explained why no body was found. This theory finally went out the window at the very end when he and the murderer were finally in the same room, and then the priest entered the picture and spoke his piece (which confused the heck out of me at first).
So, I guess what happened is that the priest decided that the girl was possessed by the devil because she had murdered a dog and done other evil things, so he ordered the workman to kill and bury her at the same time as he buried the dog. When she dies, the spirit possessing the girl then leaves her body and possesses the old man, which is why the cat won't come back to him for a long time and why the newspaper delivery kid is scared of him. This is finally manifest for us the viewer when the old man kills the workman. Although it is shown as if the girl herself is doing the killing, it's actually the old man possessed by the evil spirit that had formerly possessed the girl -- which explains the final twist ending when the old man kills his cat. He does this because he's possessed by the same spirit that drove the girl to kill the dog.
Is this pretty much the accepted explanation?