Things that I want are....
Sapphire screen. So we dont have to bother with screen protecters
Even better battery life
These.
I'd also like to see them pull away from the plastic materials and move to something a tad bit more durable. The battery cover on the Note 2, coupled with the way you take it off the phone, makes me feel like it's going to crack if I'm not careful enough. I'm a mother, of course my kid is going to play with my phone, and so durability is definitely a plus for me. I'm aware with more durable materials also comes more weight. Not to mention a bigger battery also means more weight. But surely there are lighter, more durable materials Samsung could make the Note 3 out of other than flimsy plastic...
On the S4 concept video, there was also a projected keyboard. I think this would be great, especially if they continue with making phones bigger, not smaller. I want to be able to put my phone on a surface and type out stuff without having to worry about a physical attachment needed. Kind of like the S Pen--it has a spot on the phone and you're only carrying one thing around rather than the phone and stylus separate. Make sense?
Better camera of course. I'm a mom, I take lots of pictures. I don't always have my Nikon on me, but I don't want to groan every time I pull out my mobile to capture a moment because I know it's not only sub-par, but significantly so. Especially where zooming in on a subject is concerned, the image starts to become grainy. I'm not saying the Note 2 camera is god awful--I've gotten some pretty good pics from it--but I'd like to see better. Good enough that I can sell off my smaller digital camera without a worry.
The battery was mentioned. I love my N2's battery life. It goes all day without having to be charged in the middle of the day, even without being rooted. I hope when developing the next Note device Samsung keeps its battery at least proportional, if not better. I cannot express how annoying it is to be forced to plug in a phone during the day. That would be a deal-breaker for me.
Internal memory. I've seen many people complain of no longer being able to move their apps to their external SD cards. And a lot of people are app-happy.