Here's my two cents:
I just lost interest at about, I think, Chapter 12. If I recall. Whichever chapter gives you access to the fairly open, non-linear map where you can start doing missions.
Here's my problem: I was pretty bored overall with the game until I hit that point. At least the linearity of the game focused me enough on a clear goal that I could pave forward despite my boredom. As soon as I realized that the game was about to give me twenty different goals to complete (in the form of 19 missions to 5-star and 1 path to progress forward) I sort of just said "Screw it". I knew I'd have to grind up myself some levels and I couldn't face the prospect of doing so given my current opinion of it.
Basically, I recognized that the combat system was fairly shallow and it wasn't going to get much better, and the story itself just wasn't interesting me.
You see, I didn't want to sit there facing jellies and penguin-bird-things all day, so I figured I'd take on some Wolves or Greater Beast(-y thingies). Of course, the game has absolutely no penalty for failing over and over, so I figured I'd master taking on extremely tough enemies until I could 5-star them. Of course, its more luck than not, but it's doable given the right timing if you can just stagger the right enemies at the right time. Chain-launch the Greater Beasts and you can take them out before they stand and heal themselves.
On one hand the battle system creates an illusion of complexity, but on the other its just a glorified "Simon Says" game. Simon says, switch to MED/MED/SEN. Simon says, switch to SAB/SYN/SEN. Simon says, switch to COM/RAV/RAV. Simon says, switch to RAV/RAV/RAV. Simon says, switch to COM/RAV/SEN. To make sure of the job, of course, be sure to switch paradigms every ten seconds so your ATB bar gets a free refill, and auto-battle by default since no human can input commands as fast as the computer can, unless it's just to spam a single move (blitz-blitz-blitz). Even if you know the enemy is weak to lightning but don't have it scanned, you're wasting valuable time where your ATB bar doesn't fill while you sit there dilly-dallying.
You know exactly how to win every battle at the outset, and given a particularly tough battle, victory is a combination of luck (the enemy doesn't hit you anything particularly dangerous) and timing. 5-staring battles underleveled is basically a "sprint for the finish, all or nothing, no healer or buffs" dash where you retry the moment anything goes wrong. 5-starring battles overleveled is a combination of (ab)using particular equipment that doesn't increase the maximum time... and a "sprint for the finish, all or nothing, no healer or buffs" dash.
Was there a sweet spot I missed? Perhaps. Sometimes buffs are important: your default position is usually "buffs on", but most battles are 5-starred without them once your timing is down.
Overall, the story itself has its ups and downs. Vanille is everyones least favorite 21-year-old voice actor trying to play a 14-year-old sounding girl (that's really 19 years old according to the manual). The other characters do develop somewhat: Snow warms to the player with his badass "fall fifty feet then carry someone on his back five miles moment", Hope goes through an uplifting transition but only really because that's the only direction he could have gone (it's not like you could have made him more whiny and annoying), Sazh has a mini-struggle beneath his calm and positive demeanor... but the female cast is lacking. Vanille is pure eye-candy with a backstory added for the sake of completeness, Fang has no real role (so far), and Lightning just sort of stays aloof except for one moment when she cries to Hope about her feelings.
The story is still a definite improvement over 12, which just gave each character an intro and a little motivation for joining the group, and then went off in some long-winded plot tangent that was completely irrelevant as far as most of the characters were concerned or bothered to express. I suppose I'm used to traditional Final Fantasy where the hero gets their spotlight throughout the story, and secondary characters get a bit of an introduction as they are introduced and some development along the way in the form of dialogue and commentary, with some extras and optionals thrown in to flesh them out. That was a fair way to do things: from what I see, 13 gives the characters some more introduction and some meaningful development along the way, but its sandwiched in the beginning and middle. The old FFs were episodic in a sense: they created their main interaction between characters by introducing some sort of small challenge or goal in the context of a larger goal, and having the characters talk about it and share their opinions as they overcome it. This allowed them to actually develop as characters.
This one splits up the characters and has them do some really exciting things right away, but I find myself missing the moments like the Black Mage village of FF9 or being trapped in the Casino in FF7: a change in scenery, pace, and mechanics. More memorable are the moments where you return to an area you previously visited and do things even more exciting, like in FF7: going back into that portside town where you originally took the boat ride and being captured/trying to escape, or returning to Midgar and fighting the Weapon.
FF13 does away with the "overall, fairly clear goal" and "episodic challenges" that you see in FF7 and FF9 and goes for a more "changing or unknown villain" and "fairly linear path" method of FF8 and FF12. The overall motivation is fairly unclear, and even the protagonists are slightly confused as to what to do, so the game has to give you a straight line from A to B to walk along in order to keep you motivated. Where FF7 was well-paced, with the episodic challenges varying in importance and climaxing at about every half disc, FF13 is almost a roller-coaster ride that always falls down: by the end of it you're bored. It just rises and rises in impact and significance and almost never slows down for a moment: you really have to give the player a reference to compare to, a moment in the story where things are slow and lackadaisical, or funny and joyous, for those action-packed or tragic moments to hit hard.
FF13 just struggles at basic storytelling conventions where its predecessors excelled or at least functioned (depending on who you talk to), and when the gameplay isn't much it's hard to appreciate it.
In any case, I'm bored of FF13, and I probably won't get back to it for a while.
