There are only three things that need to be done.

1) Option to skip the long summon spell cut scenes
2) Lets get crazy with materia. Combine lighting with fire? How about lighting strike that explodes into flames for more damage? 4x Knights of the Round Unlocked!
3) More materia! Add Aero, Water and other new types. New Summons. There was a lot there but you can go back and do some really ludicrous things for pure fun.

I think changing the rest of the game would really lose the charm. I like the pipe cleaning Popeye arms. I like the typos and crap. Over time it has all added up to become classic and helped to engage the community. If anything, add some more enemies or optional dungeons. FFVII was fairly packed with extra stuff but you could always add more.