The Legend of Zelda is my favorite video game series ever (and may it continue!), but I do have some issues with it.
1. Frequency of Games/Cheapening of the IP
While this isn't a critique of the games themselves, it's something that worries me. I hate Mario. I hate how overdone Mario is, and I don't want Zelda to go in that direction. Spin-offs like Triforce Heroes and Hyrule Warriors worry me. I get that a lot of people liked HW, and the only reason it sold well is that it's "Zelda", but that sort of thing, imo, cheapens the franchise and the name "Legend of Zelda". I would rather see just one, maybe two, core Zelda games a generation, with all efforts and resources thrown at it, making it an incredible experience, rather than having two or three for console and then two or three for handheld, even if they're not developed by the same developers.
2. Plot
We all know Zelda games aren't centered about engrossing stories, deep plots, intricate lore, or anything like that, but at the same time, it's time that the game take a break from the old formula.
Hmmm... my biggest problem? It's always the same plot. Link grows up on a farm/village, becomes chosen, collects certain items, Ganon is revived and kidnaps Zelda, and you discover the Trifroce... I feel Zelda should take a leap and try something that is fresh and new without losing what makes it Zelda.
It wouldn't hurt to do something different. I think having an open-world, as Zelda U is saying it has, is a good place to start.
This plot issue is especially true now that Nintendo have shoe-horned an official timeline into the series. It's so absurd because very few of the games have had any sort of continuing lore. As much as I've grown to dislike the series, the Elder Scrolls still has one of the (if not The) best in-game lore of any series. I've spent literal hours reading Tamriel history books, trying to piece together what happened during the Dragon Break, for example. I'm not saying Zelda should follow suit, but if Nintendo insists on an official timeline, then it's time the games start having a little bit of a better story.
3. Voice Acting
For NPCs, at least. Other games do this just fine. Again, I use the Elder Scrolls as an example. The NPCs are all voiced, but the PC remains silent, answering through text. Link, the player, doesn't need to talk, but it's 2015, and I feel that the NPCs should. However, this isn't a deal-breaker for me. It's just something I would enjoy, and that would make the game more immersive, I think.
4. Save Points/Spawn Points
I think saving should be available anywhere on the map, and that loading a save game should start you where you saved, not a predetermined location based on where you saved (i.e., if you save on the overworld, you spawn in Kakariko village).
Also, enemies shouldn't respawn as quickly as they do. If I leave an area, that shouldn't mean enemies immediately respawn. If I completely clear out a dungeon, I should be able to leave for a bit, and not come back to it infested as if I had never been in there.
5. Concept of Time (Game Specific)
If the game is going to have some sort mechanic where time actually passes, then it would be nice if it didn't go super fast (like in Ocarina of Time — note that I'm not complaining about the game, it's an N64 game after all) and if time had an effect on the world and NPCs. I don't necessarily mean that every NPC should have a schedule, and that they do different things at different times, but going back to OoT, at night different enemies came out than during the day. And also, I would like to be able to experience the time change, not like in Wind Waker where time stands still if you're in a town or village, but progresses naturally in the field.
Again, this would be game specific, and again again, this isn't a deal-breaker, but it's something I would enjoy, and that would make the game more immersive, I think.