Although I haven't beaten the demo yet, there are a few things that stood out right away:
The name entry at the beginning feels clunky. It's a minor thing, obviously, but I noticed it, so there you go.
You sometimes get into fights while transitioning from room to room before the transition is done, and it looks and feels weird.
The trees in forest town have touching limbs and it makes me sad, because they look odd as a result!
I do not like the tiny chests, but I have a weak spot for the old FF: Adventure style and nothing will ever change my mind, so... personal preference?
Otherwise, it's a lot of fun! I especially like the ability to control the mutation of the mutants, as originally they were such a lottery that it was barely worth playing at them. I haven't tried monsters yet! Second playthrough? Almost everything I've seen as been extremely close to the original or spot on, and it's taking me back to yesteryear, endlessly grinding toward SMGs, then Vulcans, then getting the shit kicked out of me by Samurais...