Just finished episode 4, so I'd like to offer a speculation on Battler's death at the end of the episode. Recall that in red, Beato said; "Ushiromiya Battler, at this time, I will kill you. And right now, there is no one on the island other than you. The only one alive on this island is you. Nothing outside the island can interfere in any way. And of course, I am not you. However, I am here now and will kill you." This statement presents an interesting problem with regards to how he died, as it rules out suicide or accidental death. I'm not sure if anyone's tried tackling it in this thread yet (haven't read 54 pages of replies), but I'll take a guess at it.
Spoiler for Furthermore:
We know that Kyrie and Asumu conceived around the same time, that Kyrie thinks she had a miscarriage and that Battler isn't Asumu's child. It wouldn't be that farfetched to assume that the current Battler is Kyrie's son and that Asumu's son is either the culprit or accessory to some of the murders (assuming she successfully gave birth).
Now this may sound ridiculous, but hear me out. Let's say that the real Ushiromiya Battler (Asumu's son) ended up in Kinzo's orphanage, was trained to be furniture and ended up serving the head house.... as Kanon, whose real name we still haven't been given for some strange reason. In this way, the red statements that only 17 people are on the island, "Kanon is dead" and "Ushiromiya Battler is the only person on Rokkenjima" are not in conflict, as the second statement could be interpreted as true in a purely semantic way if we also equate the death of a personality as "death." Thus, we could say that the furniture personality "Kanon" died and the human "Ushiromiya Battler" was reborn and murdered the Battler we know to explain the last death in episode 4. If this sounds dumb, I apologize, but I find it jarring that Kanon has had his corpse disappear at least twice and required his death confirmed in red more than any other character.
I have some ideas how these might factor into earlier episodes, but I'll explain them a bit later.