I can only hope that Square Enix had their ears open after FF XIII's launch. They need to fix everything that eroded the review scores and the fans' faith in the series.
1) Linearity can work, but straight corridors with forced encounters are no better than the random battles of old.
3) Story and characters. The characters certainly look the part. But aside from the overly complicated outfits and some oddly sexualized characters - I'm looking at you Vanille - the characters don't really hold my interest. Sure, they've all got reasons to hate being Fal'cie, and the framework for interesting back-stories is built, but everything is laid out on the surface. It's like the characters are a list of traits that only run skin deep. This goes for the entire story. Square Enix gave themselves a lot to work with here. They've created a visually striking world that's full of tension, but the plot twists and turns before we are given a chance to care about Gran Pulse and Cocoon. It seems like complications are thrown in just for the sake of making the plot complicated.
I have faith that Square can still create a stellar sequel, but they need to go back to the drawing board in some respects. They've built a beautiful world with an intriguing premise, but now they have to build farther by allowing players to explore and become connected with that world through game play and story.