I see the "Manage Push Notifications" option in the app's settings, but there are only four choices for the notifications you can toggle on and off: "Close friends list activity," "Group posts and comments," "Tags you in a post" and "Mentions you in a comment."
My problem is that I'm getting notifications every time friends (usually close friends, not always!) post anything on their profile. I'm also getting notifications when someone leaves a comment on a post after I do (regardless of whose post it is). I don't see options to turn these things on and off but they're driving me crazy!