Dawson Casting: A rather extreme case: Kathryn Beaumont, who voiced Alice and Wendy in their respective films back in the 50s reprised both roles in this game despite being in her mid-sixties at the time it was made. Naturally, her voice and performance sounds very different and rather unconvincing in the role of a young girl.
No Export for You: Final Mix initially wasn't released outside Japan due to concerns that Americans don't like buying the same game with only a few extras added (which isn't entirely an unjustified concerned, looking at you Capcom), particularly bad because it actually added some pretty vital plot information that set up the sequel. But it's now confirmed for release internationally as part of the first HD collection for PS3.
The original concept for the game had Mickey as the main character, with Donald and Goofy helping out. The development team eventually became divided on whether he or Donald got to be the main character, and so they compromised by creating Sora.
Sora's original design was more lion-like and weilded a chainsaw sword. This was changed to a giant key to be less violent.
Many early screenshots for the game showed Donald and Goofy wearing their classic outfits from the original Disney shorts. This was changed to the current attire they wear in the game, presumably to give them more adventurous appearances, and they can only be seen wearing their classic attire in the game's epilogue.
Chernabog was going to be the final boss, as the embodient of all darkness (being well, an ancient Slavic god who has power over death). This was changed for various reasons.
"Destati" is apparently considered cursed by the production team due to odd incidents—the worst being the entire building losing power—occurring whenever the vocal track was inserted into a piece of background music.