Here are some things that I believe should be added to Miitomo.

Favorite color! The default favorite color is chartreuse and unlike its Mii maker predecessors, there is no way to change it, and it will stay chartreuse if you link it to a Nintendo account.
Better camera. I made my Mii from scratch, and it wasnt long before I discovered that the camera software was...a bit less than I expected. As in, half the time it thought my eyes were closed. At least it can detect glasses now.
Gifts! In Miitomo you currently can't get rid of clothes. That's why I have 3 pairs of princessy pearl slippers I don't need. If you have clothes you don't like, I think you should be able to give them to a friend or sell them. It would be great if you could give your friends coins or candy too.
Movies! Call me crazy but I think it would be awesome if there were a Mii movie maker in Miitomo. Mostly because I really want to animate something with Miis in it.
And I would also like to include my Miis in reaction GIFs. 
I will be adding to this list.