I'm loving the game so far. One of the complaints I've been reading about the game is that they find it hard to get attached to Jodie and feel for her, but I've had no problem with this. Ellen Page has put on an incredible performance so far. As for the story overall, it's definitely weird, but I'm kinda into it. Once again, this is due in part to how fantastic Ellen Page is as Jodie. Games need more real actors instead of the people they pick off the streets. My only complaint with the story is the telling of it -- the story jumps all over the place, from Jodie as an adult, to Jodie as a kid, back to Jodie as a CIA killing machine, back to angsty teenage Jodie, and so on. David Cage made it almost impossible to really follow the story.
The other problem I have with the game is the controls and camera get in the way of each other occasionally. You'll be walking in a room, holding the analog stick forward, and then the camera will cut to another position where you have to hold the analog stick left to keep moving in the same direction. If you don't change the direction of the stick quick enough, you'll walk right back into the other scene, and you'll be stuck switching between the two different camera positions as you try to determine which way to hold the stick.
I'm probably a little over half way done with the game, but I'm digging almost everything I've played so far.