Story/Characters
I've so far (Ch11) found it to be all characters no story. Quite frankly I am getting tired of drawn out character exposition. Not to mention we know nothing about any characters other than the main party. I'm usually a plot development > character development type of guy, but I am willing to chalk up my growing disinterest in cutsceens to personal preference.
I don't like the idea of a scene at the start/end of a chapter. Dividing games into 'chapters' really seems to make the story seem un-natural and contrived to me. I feel the story should always be ongoing. Think back to previous FFs. The idea that they could only stop to talk at set intervals would be ludicrous.
Linearity
I don't mind this all that much, I actually really got turned off when it opened up in Ch11

My main beef is that nowadays it seems to be a choice between straight line dungeon and wide open dungeon. Both are not intricate and I find them equally uninspired. I personally like random battles better than ones that appear on the field map, but I don't think this system is appreciably worse.
Stagger
Buff/Heal/Damage? Isn't that what happens in EVERY Final Fantasy title? 'Random' battles are a chore if you just try to plow through them, the fun is to experiment and try to make a strategy that downs them in as little time as possible. If you aren't interested in that, well, yeah the battle system would blow for you.
Crystarium
Yeah, the whole thing should have been opened up right from the start. I don't see the wisdom of capping it every Chapter, since the costs increase exponentially it isn't like you can easily power through to the end of one at the beginning of the game. The real reason I suspect is so they know what every character would have and can tune the encounters accordingly. If you cap out Char A in RAV you might as well put the extra points into MED, but if it was open you might not bother. And then be screwed when you have a party switch and have to depend on that character as your healer.
Characters
Lot of Hope hate going around and I agree with it. Other than Hope I don't strongly dislike anyone in the game, which for me is doing well. I love Lightning as a character, probably because I also liked Cloud as a character. Also her animations are awesome.