1) The main character tends to take a lot of side quests from people that have nothing to do with his main quest, and Grimoire Weiss (the talking book that acts much like D's hand in Vampire Hunter D) tends to ask the same questions an outsider watching the game would ask: "why are you taking this quest? What is the point of this? You're wasting time." The conversations take place as you're traveling around, and they tend to be both humorous and build a rapport between the two characters. Weiss is not just a Navi character. He's a pretty bright part of the general dialogue.
2) There's a mystery that I haven't quite unraveled, that has to do with the distant past (our near future) involving (seemingly) the main character and his daughter. When the game first starts, loading screens tend only to be diary entries written by the daughter in the present day of the game, but soon they're interspersed with what seem to be medical entries dated 2016-2020 (1300 years before the main game takes place). There's a great trickle of interesting but seemingly unconnected story that's slowly being uncovered as I venture forth in the game.
3) The story is unrelentingly bleak. I don't mean violent, and I don't mean savage. I just mean bleak. There's an element of hopelessness that is missing from a lot of JRPGs, and it's very refreshing.
4) The story is, at its core, a touching connection between a simple man trying desperately to save his dying daughter. It's not overly soppy, and the player is never beat over the head with it, but the more time you stay away from your house adventuring, and the more you read diary entries in the loading screen, the more you realize that helping and trying to save your daughter is synonymous with leaving her alone to fend for herself. Being a good father essentially means being a bad father (which, having grown up with a father who traveled 3 weeks out of the month, is a very essential dichotomy I know all too well).
I'm not too far into the game, so I'm still not into the meat of the game, but that's what has gotten me so far.