I think more emphasis should be put on puzzles as a whole, but if we're talking about specifics then I have a few ideas.
For one, there needs to be more "individual" puzzles, you know? The standard ones you would see in Dungeons? Basically I feel they're somewhat hard to find in modern Zelda. For example, a typical one would be were you have one room dedicated to one individual puzzle -- think the ice block puzzle or even the picture puzzle in the Forest Temple, but obviously the designs would alternate. My point is, just more of these specific puzzles, also it wouldn't harm us to have more in the overworld as well.
Then there needs to be more implementation of actual puzzles with basic navigation. Walking, running, rolling, riddin; are all common forms of traversing the world, but yet they are rather simple and less stimulating. If the game makes the player think on how to proceed then it makes overworld navigation, not only harder, but more stimulating -- basically just making the player think more. I would refer to "duel overworlds" here, the Dark World in A Link to the Past , the past and the present in Oracle of Ages and the seasons within, obviously, Oracle of Seasons. Combining puzzle elements on such a large scale made navigation a task rather than just a simple stroll and it gave a sense of challenge to every path in the world.
An idea that I had, was an ever changing structure -- possibly a Dungeon. The is just a possibility that I have had floating round in my head revolving around Dungeon-design. Basically the Dungeon would alternate it's entire structure based on specific movements and times. This would make one typical Dungeon playthrough very different. It would be an advanced idea of a maze but the structure would change all the time -- leaving you in different rooms without you choosing to enter. The player would have to figure out how to navigate effectively, they would have to figure out just how the Dungeon structure changes, counteract the changes as well as figuring out navigating the structure. Think the Sky Keep but a lot more complicated and a lot more changes.