Definitely a graphics upgrade. Most of the backgrounds are perfectly fine, they'd just have to work on the characters. Upgraded and additional cutscenes would also be nice. And I would like to see some voice acting in it, as long as it was done well.
I don't want them to just delete the entire FFVII storyline and rewrite it, but an accurate translation, and clarification of the storyline would be nice. (It's kind of sad that it took me 12 years to find out certain aspects to the story due to mistranslation and unclear lines.) I want them to keep the humor and language of the original though (i.e. don't take all the cussing out of Barret and Cid's lines).
Make Vincent and Yuffie mandatory. This would require slight changes to the storyline, but I'd be ok with it. If they were made mandatory, they'd be included in cutscenes and conversations. I still also say, that Vincent should be required to go with you to see Hojo near the end. I wonder if any FFVII fans watched AC and went, "who the heck are these two random people? I've never seen them before!" XD
Make Aeris' death more emotional. It bothers me how after she dies, Cloud buries her, and that's it. Then it's Cloud in the shell house talking about himself. I see it as, your friend/companion was just randomly murdered and nobody really reacts at all?? And I wonder if they'd ever address the whole, "why can't you just use a Life Materia or Phoenix Down"? XD
Also, to a lesser extent, I wish they'd clarify how they got ahold of the Highwind. It's just kind of like... Shinra's out to get them, but somehow the party gets ahold of Shinra's airship, and there's no fight about it really, nor does Shinra come to even attempt to get it back.
More dungeons, or expand existing dungeons. Chocobo Breeding is a pain, but it's kind of silly how easy you can just walk into those caves and right there, Knights of the Round or whatever super-power Materia is just sitting there. I think it would be interesting to expand those caves and make them dungeons where you've got to fight a boss before you can get the Materia. More Underwater exploration would be nice too.
Northern Crater: when you split the group, they should make it where you control two parties and have to guide each one through. Anyone who's played FF6 knows it was done in the Phoenix Cave and Kefka's Tower.
I'd love it if they let us choose anyone we wanted for the party at the end of the game. I could see limiting it and forcing Cloud to be leader to go into the final dungeon, but for exploring and level grinding, why not let us choose whoever we want?
I'd like to see them change the ability system/Materia somehow. It always bothered me how it didn't matter who you had in the party, because everybody could learn every skill, and if you had a high-level Materia you could just swap it and anyone could have all the best skills. Maybe the best thing would be to somehow make it where each character has to level up the Materia themselves.
Expand and improve the Gold Saucer games. Keep the Snowboarding, I loved that game! If they added something new, I'd love to see either: a Pinball machine, or a shooting game.