Ooooh, I feel younger me would have a trip day coming up with ideas for the games.
Out of the gate:
I saw something just today where people were saying "If Nintendo releases OoT and MM in a combo pack with better visuals, they should have Majora's Mask take place directly after, and it let you enter the lost woods to better connect both games. With the ability to go between both at will.
Sounds like a fun idea that I would have loved back in the day, or as a way to package both games together. It sounds cool but you don't really see the company taking that much effort for it. I'd love to have the entrance in OoT's lost woods. I just think the time lapse between the end of OoT and the beginning of MM would have that Nintendo would need to build. Imagine after the "The End" cinema visit from Zelda (and the rendition to your song) the game starts again with you from your house, just like any time you are a kid outside the dungeon. It'd be cool to go to the Lost Woods, but I'd prefer we get something motivating us to go there. It'd be neat if the opportunity was used to bring the emptiness of Link that moved him to embark on the journey to search for his friend so once that you know he's doing that have the Lost Woods have a new area, maybe towards Faron forest or something that you are instructed to go as a possible clue of Navi whereabouts just to ultimately stumble upon the familiar start of MM.
-Items for all forms: While each form is great in its own regard, why are the items they can use be limited to just bottles? Why not let them be able to use all items and masks? Maybe we could even give each form its own version of the item in question (masks would be the same across all forms).
I remember I used to wonder why that is not the case. I thought back then that perhaps they were afraid f rendering "normal" Young Link pointless if you could use everything on every form. The forms already have unique habilities and properties like for example their weight, so maybe it was an artificial way to make Link in his human form more needed. I would love to see the items adapt to different forms in a similar way that the Ocarina of Time does. Masks staying the same makes sense, haha.
-New masks/mask properties: Examples include a Stalfos Mask to turn Link into a Stalfos (replacing the Captain's Hat), the Stone Mask letting you turn invulnerable, the Garo Mask taking on the Stone Mask's properties as well as its own, the Fierce Deity's Mask being able to be used everywhere, the Couple's Mask doing something, the Boss Remains and Majora's Mask itself being wearable, and more.
I definitely would be up for new masks or expanded uses on the masks. Give me more scents to track with the mask of scents. Give me more reactions from people while I am wearing distinctive masks.
I like the Captain's hat, and I don't think it needs replacing with the Stalfos to have that ability annexed to it as a reward for beating the race on Ikana.
I think that if you defeated the game once with it, then unlocking FD outside of the dungeons would be a cool addition.
-Upgradable everything: A Skyward Sword thing carried over here. Speaks for itself really.
That's an interesting idea, I just wonder what would be good to use as materials, since the insect collecting is not present, but the game already has the masks themselves to collect, and not everyone would welcome having to go around collecting other new elements to shoe-horn it. I think depending on what we need to gather and how enjoyable the process is merged into the game's already established mechanics, that could be neat. I especially would like this idea combined with moving with the OoT inventory, and that way carry unique weapons to upgrade in MM.
-New Game +: If you don't know what that is, it's a 2nd playthrough where you have everything you collected from your previous one, but everything's harder.
It's always neat to have a Hero mode in Zelda games, not sure if having everything from the beginning would go well with the first part of the game, but considering that you already went through the story once before, it is not a big deal. It would be neat to get the extra challenge.
I need to have a good think about what I would like too so you guys can take a knock at my ideas and tell me how little feasible they are. 
Personally, because Link is coming from Hyrule, I'd like his Kokiri Sword and shield were the ones from Ocarina and then that he'd get the upgraded version in Termina and that the wooden shield gets destroyed as normal with fire, but I guess that's dumb if you are a first-timer and you can't get it back, unless it is a part of cutscene or something.
It doesn't count as an upgraded I guess but I wish that if they bring it to the switch that they restore Mikau's swim ability the way it was on the Nintendo 64.
I'll try to think on more...
