Just reporting a bug here.  If you haven't played through the game yet, probably don't continue reading.

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Following the final fight with Gilbert, I realized you don't actually have to touch the lantern to end the game.  Gilbert's area becomes unlocked and allows you to leave the boss room.  If you do, the game visually shows your life total to be zero, and for some reason most of the enemies of the game stop responding to your presence.  At this point, you can return to Gilbert's boss room, touch the lantern, start a new game, and this glitch carries over into the NG+.  I've noticed that it seems enemies with scripted fights will still respond to you, but normal enemies don't react at all.  I'm not sure why this is, but it's apparent there's some deeper issue going on.