I'll be completely honest, I thought that Skyward Sword was amazing the first time I played through it. However, reading this thread has made me think of what else this game could be to make it truly soar (no pun intended)!
That being said, here is my list:
1. More regions and dungeons. The fact that there were only 7 dungeons in the game, while definately challenging, felt too short and too confined. I feel the same as many when I say that an ice region and an ice dungeon would have been beneficial to the game.
2. More in the sky. The sky felt very barren, and reading some of the comments on this and some other threads has made me think of what else could have been done in the sky. Perhaps another island full of people, or a "Cave of Ordeals"-esque island where you could fight through progressively tougher enemies (maybe as a part of the Thunder Dragon's Lightning Round?). Maybe there could be a dungeon in the Thunderhead, where you find out what has happened to Levias before you fight him. These are just some of the things that would make the sky feel more alive.
3. More/Better minigames. Fun-Fun Island, which is one of the only minigames I can really remember playing, was very time-consuming and tedious. I wish there would have been more minigames on the surface, as I can't even think of any off the top of my head. There was a minigame for your sword and your bow, so why not take it a bit further? Have a minigame with the bombs where you can "bowl" Bokoblins down! Or have a minigame with the whip where you need to grab certain items to get points. Just expand it, but in a way that would not feel like you were just padding the game's length.
4. Expanded customization system. This one is just nit-picky on my part, but I would have loved to had more of the customization and upgrades. Other people have suggested upgrading your tunic for different situations (eg. Fire/Water tunics), or upgrading your bottles for more capacity. That would have made more sense as far as the "+ +" upgrades go, because you have the same amount of space in your bottle, so why would you suddenly be able to hold twice as much potion? Also, make more upgrades required so that there is a reason to pick up all of the treasures that you see (with the exception of Amber Relics and Jelly Blobs).
5. The ability to mix potions. This would have really fit with the customization theme well. For instance, the Revitalizing Potion restored your shield meter and restored a few hearts. What if you could combine that with the Guardian Potion so that after you've restored your shield meter, it doesn't go down for a certain amount of time (essentially making your shield "invincible" for a few minutes)? This, combined with the bugs to upgrade potions, could make so many different potions for so many different situations.
6. More enemy variety/better enemy progression. It seemed that it was the same enemies throughout the game. Where were the ReDeads? It felt like there were not very many enemy types in the game, and I wish that there was more variety. As far as progression goes, there is very little change in the enemy difficulty throughout the game. Mases complains about this many times in the video walkthrough, and I must say I agree with him.
7. More exploration. The game felt very linear in the fact that there wasn't really anywhere to explore freely. It was basically just a path that you had to traverse to get to the next area with little to no secret areas. There wasn't much to really explore, which is a shame. Perhaps adding in some areas between the three (or in my ideal SS, four) regions in the land below to get from one region to the other without going back up to the sky would have added to this.
8. The ability to fly and explore the land below at night. This is one that I would have loved just to see new enemies and the same locations with a completely different feel to them.
That being said, this was a very nit-picky list of things and adding these would just make an already great game even better. I would love to see another Skyward Sword-esque game with these features added, though I know that will likely never happen!