Man, after I promised myself I would stop posting in FFXIII related threads you had to make this one...

Where to begin:

Better control of your party: Like Karifean mentioned, either give me the ability to switch between characters in battle or give me control over setting up the A.I. so it's less painful. Better yet, just do both. XII had the right idea about A.I. party members.

Better party diversity: For a game that tries so hard to make every character a specialist in at least one field, it does a lousy job. I feel the biggest issue to all this is that some characters are seriously not as useful as others. I never use Sahz as a party member despite being my fave character and the few times I try to use him, I always regret it. I like using Snow, but Fang outclasses him at almost everything, even Ravager which is not one of Fang's primary classes. Vanille is completely outclassed by Hope and only maintains some usability because the makers decided to give her the most broken ability in the game that makes most of the difficult Mark Hunts easy and farming Adamantoise' much more bearable, beyond that, she's a poor man's Hope. Lightning has main character syndrome, in which she's good at almost everything, sure she's a lousy medic, but she's better than the three who don't naturally get the Role and she's the second best Ravager in the game and debatable the second best Commando. Making her the perfect secondary character to Fang and Hope who are the best in their respective fields.

This leads to a party of Lightning, Hope, and Fang which funny enough, the game has a tendency to make your default party in several of the later chapters. It's like the creators wanted you to only really use this party. Even the weapon abilities don't add enough reason to ever use the others cause often times the main three have just as equally broken abilities that make them more useful than whatever skill makes the others characters less lackluster.

Main Character equals death: Normally, this doesn't bother me but when the game sends you into chapters with frail characters like Hope and Vanille (even Lightning is pretty damn flimsy tbh) and the customization system/battle system offers no real way to protect said character effectively, then it gets annoying. The Barthandelus fight is often said to be one of the hardest battles in the game but for me, what made it so difficult was the fact the boss eventually cast a un-removable death spell on your lead character that makes the battle one about speed. I could have beaten him the first time if it wasn't for this spell and rule, cause my party could hold their own against his other attacks. Its especially grating cause their is no damn good reason why your other party members can't save them.

I begrudginly accept this in Persona cause your main character is basically a one man army who really doesn't need the other pary members, and in normal SMT games, it makes logical sense cause your "party" are being that you summon, so wiping out the summoner ends the summons obligations to summoner. XIII neither has a story reason nor does it have an effective gameplay set-up to make it manageable. What makes this especially annoying is that the game isn't really all that hard so when you die, it always feels like you're just being cheap shot by the game instead of legitimately being overpowered or outflanked.

Better Equipment Set Up: I kind of like leveling equipment but the whole idea looks better on paper than in practice. Part of the issue is that you rarely need to improve any of it with the exception of the Barthandelus fight mentioned above, and improvements never feel meaningful cause when it really comes down to it, your characters stats matter more than their weapons in determining damage and how much damage you take. It feels like FFX all over again where beyond a few certain abilities, weapons all feel the same and ultimately its leveling the character that is more important in dealing damage. On the brightside, the skills are more useful, and the game isn't as piss poor easy as FFX so at least weapons feel more relevant if only for the innate abilities and the poorly explained equipment affinity bonuses.

The other issue is actually leveling said equipment, the games system is retarded cause it barely gives you enough material from drops to make any meaningful leveling. Beyond rare items that are used for evolving weapons and the few scant items meant only for leveling, nothing in the game gives you sufficient enough funds to buy the materials needed in bulk, and most of the items don't give great XP beyond a scant handful (that is expensive to buy) and even then you need to have a max modifier to do get that measly amount of XP.

The easiest ways to fix this is to either
A) Have enemies and treasures give you better bulk of said items.
B) Increase modifiers (up to 10x would be nice) or increase the amount of XP items give or lower the cost of upgrades.
C) Don't use a loot system to gain money and just let everything drop money like the old games so every battle can net you cash to buy materials more readily instead of farming the few enemies that drop high resalable items.

Make the game less Linear: While I have no problems with the open ended environments of XII and much prefer them (Which Looney BoB and VeloZer0 will both most likely chime in to say they didn't care for.) Just some options would have been nice, not a simple and short road that leads to a treasure chest occasionally spread out, or the illusion of non-linearity by making your characters have to auto-jump across some rocks or the path winding in a circle. I mean some actual multiple paths that take you way out of the way with some decent treasures to reward you for going off the beaten path, or two roads that lead to the same location just take you down different visual canvases. Hell, just making the dungeons not look like a road would be a good place to start.

How about adding some minor puzzle elements a bit more, we had some in the early Chapters (1-4), but they are all gone until the end parts of the game, leaving this monotonous middle section.

Don't be a hypocrite about :
By this I mean towns, don't say you didn't put towns into the game cause the plot makes it impossible and then halfway through the game have two characters walk into a town completely unnoticed and actually don't cause a stir until the military finally catches up with them much later in the chapter when the characters are wandering through an unpopulated part of the city. You could have put in old school style towns, you just didn't cause the project was managed poorly, said town wasn't even interesting...

Better Mini-games/Sidequests:
A) It didn't really have any, besides collecting wool that does nothing, chasing a frocobo that was poorly placed in the game and unnecessary, collecting a few items to restore a robot, and the Ci'eth Stones which are a poorly utilized version of XII's Mark Hunts, the game offers very little in alternative gameplay.

The Mark Hunts are especially disappointing as their backstories are all the same (I failed at killing a big monster that I have some connection with, either it terrorized my village, killed a love one, or is a love one) but after awhile they all look the same, it's made even worse when your realize a good 2/3rd of the Marks are just normal monsters you will fight a little later as you journey through the plot (you may even fight a few of said monsters on your way to kill the Mission version), and the few unique monsters are actually reused a few times as well. There are at least four different Missions that have you fight that flying monster that spams status spells and has a high Attack power. A little better variety is not asking too much I feel, X's arena and XII's marks used pallette swaps, but at least they were all unique from each other and had different fighting mechanics.

I also don't see why they had to be left purely for the last segment of the game. The beauty of the system in XII was that it was introduced in the beginning and was used to supplement the normal journey. Some of the early dungeons could have been more interesting if you had optional mini-bosses available that forced you to learn the system better and early. You can't tell me that Cocoon's fal'Cie didn't occasionally make a few l'Cie during the war against Pulse or that some Pulse l'Cie got changed to Cieth stones before finishing there missions in the war and were brought up to Cocoon when it tried to repair the damage caused by Ragnarok.

Nor can you convince me that Snow, Hope, and Vanille wouldn't convince Lightning, Sahz, and Fang to stop and help. The three practically wear their damn hearts on their sleeves and despite running for their lives, I don't feel it's out of character for them to want to help people who were trapped in their situation. Hell, there probably could have been a way to implement this partially without even using the Ci'eth stones at all, but leave it open for the players. A switch hit at the beginning of a stage releases a PSICOM experiement that is being caged for the moment or activates a special security droid that is optional.

Of course I would also re-haul the plot and cast but we're mostly talking about game mechanics so I'll leave it at that.