One of my favorite things about Zelda games used to be the puzzle elements. In more recent titles the puzzles have been less puzzley and more unnecessary busy work just for the sake of having it. The shrine system (and the two "dungeons" I've completed) utilize logic and problem solving in a way that feels genuine for the first time in a long time. They are legitimate puzzles that require real thought, problem solving, and (in my experience so far) don't have a "wrong" way to complete them. For example, the Myahm Agana shrine? I got frustrated trying to solve it the "right" way and figured out that you can actually completely flip the platform over and complete the maze unobstructed.
I liked the addition of crafting and item durability in Skyward Sword, so I was glad to see that carry over and taken to a new level. In SS it was a bit of a novelty, whereas now they are actually a key component to the game and a major part of strategy. I do wish there was either some sort of recipe log that filled in as you made things or cookbooks you could buy. I've accidentally made epic things that I'd love to recreate, and I've made things I'd like to never waste ingredients on again. I could start my own written log, but considering the number of combinations and how long it takes to craft something (it's not really that long, but when you're doing a bunch of things it isn't insignificant) that just isn't realistic. Still, the fact that I can collect materials to create custom buffs for myself is fantastic.
There is a lot of silence in the game, but when there is music it reminds you that one of the most iconic bits of Zelda games is the soundtrack to which it is laid. I love the way that music has been utilized in the game, and while I'm sad I don't get to hear it more often I can appreciate what the silence does to the experience.
You know what else adds to the experience? The environment. For the first time in Zelda you really have an interactive environment. Temperatures, weather, wildlife, all of these are great elements to have included and bring a more immersive feel to the game.
God forbid you find something and then have a need to return to it later. Gone are the days of "hey I remember there was a dude that was by a tree in that one region let's go that general direction until I find him." Good fucking luck with that. If it didn't occur to you to use one of those stamps on your map at the time and it's not a current direct objective, I'm pretty sure you're going to have to leave finding it to your grandchildren unless you Google it. Need to find something new? HAHAHA yeah that will likely not happen on purpose. Those memories you're supposed to track down with no direction as to what, well, direction to head? What the hell. Some of them do have a landmark so you can at least identify a rough area, but many of them don't and you just have to cross your fingers you stumble that direction.
My other issue with the size of the world is that the game hinges on exploration and discovery of small details (*cough*Korok seeds*cough*) and it is simply too large to realistically be able to do it. Yes it's possible, but you shouldn't have to spend hours upon hours doing nothing but canvassing the world in order to find all of its secrets without looking up a guide.
Short version? In the normal course of completing the game you should discover at least half of what the world has to offer. The size of the world, especially compared to the sparse number of main quest objectives, is too massive. Even with a "reasonable" amount of exploration you barely scratch the surface (example: a friend has reported they are 100+ shrines and 100+ Korok seeds in, having completed the main quest line and progress shows as only 28% complete).
Like SS, while it can be annoying to have your equipment break I agree it is a good feature that forces the player to really consider the risks and rewards of a battle and to choose weaponry with purpose. Knowing your equipment is going to break and knowing there are places you don't want to take certain items (metal in electricity-filled areas, wooden items in fiery places, etc), it's a tragedy that there isn't a storage solution for your extra items. Even the SS system of having to check your items with someone at a set location would be preferable over nothing.
On that same note, the frequency at which weapons break is RIDICULOUS. Yes there are weapons everywhere, but there aren't good weapons everywhere and there's the rub. You can know exactly what you need to be effective against an enemy but if yours broke and you haven't found a new one, tough cookies. Trying to complete a challenge or a boss fight that needs a bow? Better hope you've got some fresh ones with you, because you're incredibly unlikely to be able to pick up a new one in the middle of the task and if you break them all you're going to be in a bind.
Do you know how many times I've accidentally jumped to my death because I was trying to, say, stand on an edge I wanted to climb down and instead I JUMP CLEAR OFF THE EDGE and either end up somewhere I can't climb out of or catch the attention of a large enemy encampment? Enough that I don't even feel bad about that ridiculously long sentence.
The horses. The horses. At first I was like "yeah this is so cool that you can just catch a horse in the wild and make it yours!" And then I was on a freshly caught one when I accidentally encountered a Guardian and he refused to run away from the bastard. So we both exploded and caught on fire. Cool element, terrible damn execution. At the very least give the horses some kind of sense of self-preservation so when an ancient technology is firing lasers at you it doesn't insist on running towards it.
Another cool idea gone wrong: whistling to get the horse/other characters' attention and have them come towards you. The AI that governs entities' response to this stimulus is so dumb I wouldn't trust it to babysit a rock. No, you aren't stuck. You're not too far away I can literally almost touch you. Why did you stop following me? DON'T RUN OFF THE CLIFF.