I myself would like to see a few aspects be buffed, improved or included in future sidequests:
Dynamic, Randomly Spawning Events
Dynamic events are somethings featured in the MMORPG
Guild Wars 2. Essentially what they are are quests that
do not require your presence to initiate, mediate or complete. They're basically like field events that happen sporadically (there's typically an invisible timer tied to these things). Now, whether you fail the sidequest has no relevance to the mainquest at large as they're entirely repeatable, but there are also branching paths. So, say that there is an event that happens in Hyrule Field where a large Iron Knuckle appears, terrorizing passerbys. You've five minutes to dispatch the foe. If you complete the quest, you get your Rupee reward, your piece of heart and other things depending on how skillfully and how quickly you took him out. However, should you fail, then the Iron Knuckle would summon bats and other enemies, leading to a different event that is a chase-based event and you simply have to
catch up to the Iron Knuckle. I am absolutely sure Nintendo can do this; the Wii U hardware is definitely capable of handling such things.
Longevity & Better Rewards
A problem I've had with recent sidequests and even those in
Ocarina of Time is that they simply aren't long enough, aren't repeatable and they just aren't worth anything. A way of increasing their longevity is simply to make them
more intense. Make fighting-based sidequests feature buffed, tougher enemies with more tricks than the base they're used on, or introduce secret bosses that are totally unlike anything you've come to expect in a Zelda game (attack wise. give us an Omega Mark XII or a Yiazmat

). Make timers be less forgiving for fetchquests, and introduce many hazards of all kinds. But, that's only the cake; we need the icing.
What's part of every sidequest, the ice cream on top of the clock tower, is the reward you get from completing them. All of this danger isn't worth it if we get a measly fifty rupees or some potion that honestly isn't worth it by the point of the game you're in. If Zelda sidequests want to be worth it, we need to get things that are useful from them or else we're just doing things for nothing (except enjoyment)!
Combat
Zelda has done combat sidequests before (e.g
Savage Labyrinth (TWW), Simon's Simulations (TMC), Cave of Ordeals (TP)), but I'd like to see the combat be upped at least twenty fold. I want to see enemy variations that are totally distinct from main quest counterparts. This means immense buffs, totally new combat styles and a myriad of different techniques they can use to rough you up. So, for example, imagine this: in
Skyward Sword you know the dreaded
Bokoblin? Well, it's annoying as all hell in the mainquest because it's a defense-monger. But, in some sort of sidequest, imagine a Bokoblin that had a sword and a shield, who fought as effectively or even more so than Link did! That would be annoying, but it would be something totally different, right?
Field enemies aren't the only thing that need buffing. If we're to refight bosses, those bosses upon refight should have attack and defense buffs, new techniques not-previously-seen before (think about
Star Ocean: Till the End of Time's Urssa Lava Cave character fights -- Evil Fayt for example has Lightning Strike, a Symbology spell that the player character Fayt cannot use) and even speed buffs. Just to make things more grinding on the gears! xD
Accessibility
A good deal of sidequests, and when I say good deal I mean the
gear grinding sidequests are only available at the end of the game, where sidequests mean absolutely nothing aside from 100%ing the game (e.g Lightning Round in SS). Great rewards have to be useful, and that means obtaining those rewards at a reasonable time period. :>
More Mini-Plot Relevance
This doesn't apply to each and every sidequest as a whole, but I would love to see more sidequests start having compelling little stories within their own little sphere. So, think about it like this: imagine a story with the grandeur of Ocarina of Time (not saying OoT's story is even decent, but it's a typical coming of age Hero story). Now, sprinkle
Skyward Sword's main quest and
Majora's Mask's sidequests on top of a great deal of the sidequests. You get your hero story which all Zelda games typically are. Then within the sidequests, you experience stories you possibly could relate to or are similar to what a real life human could do (similar, not exact). Just little things like saving your childhood friend (SS's plot at large; the theme was becoming a hero), helping out farm residents who aren't in the best of situations (MM's Romani and Cremia sidequests), or even helping lovers reunite (MM's A&K sidequest).