Things like better graphics and an orchestrated soundtrack are obvious, but I think the question is leaning more towards how Ocarina of Time could have been better when it was first released. Skyward Sword was my personal favorite Zelda game, but I still hold Ocarina of Time as the best. Skyward Sword is immense fun playing through, but it leaves me feeling like so many things are missing by the time the credits roll. Ocarina of Time doesn't give me that empty feeling, as it's essentially the most well-rounded Zelda game with the fewest glaring flaws and omissions.
Therefore, my list would resemble this:
#1: Make Epona more mobile. She couldn't touch water or hop down ledges, the jumping mechanic was a little gimmicky, and you could really only use her in Hyrule Field, Lake Hylia, Lon Lon Ranch, Gerudo Valley, and Gerudo Fortress. She was severely limited and a little hard to handle at times. It would have been nice to take her darn near everywhere and perhaps fine-tune her controls in addition to enabling Link to take damage on her, meaning you'd need skill to ride her.
#2: Implement difficulty levels. Ocarina of Time was a pretty hard game the first time around, but once you understand the controls and the enemies, it becomes pretty simple. A difficulty mode could increase enemy presence, strength, health, and/or techniques, forcing you to adapt or promptly perish.
#3: As many have said, increase the money sinks. Supplies could be found free everywhere (harder difficulty levels could adjust this), and most players probably found themselves spending money only when they needed or were guided to (i.e. Hylian Shield, extra tunic). This means more mini-game ideas and gameplay reasons to refill on supplies. A bank would also be nice, as extra money could be stored there. Perhaps there could be a gladiator-type mode where you take on challenges and bet on your outcome, such as defeating three Stalfos in one minute without taking damage. If you fail to meet your wager, you lose money. If you fulfill it, your money increases. The more battles you win, the more substantial rewards you earn (such as Pieces of Heart or upgraded wallets).
#4: Dungeons that can be redone, possibly with additional challenges like time and heart loss. Majora's Mask had only four major dungeons, but made up for it somewhat by having each one able to be played again. Ocarina of Time could do the same thing and reward you for completing challenges.
But like I said, Ocarina of Time was and still is an incredible game. There are all kinds of ways to refine it, so maybe we can hope for the next Zelda game or another Ocarina of Time remake far down the road to use these things.