I hate the glass; I wish they'd lose that (and bring back removable batteries), but not holding my breath. Really, if I could have a Note 4 with a bit of a RAM/ CPU boost, add Samsung Pay and the Iris scan, I'd probably be pretty happy. I'd rather lose the edges as well - not that I want a huge bezel, but I've never really seen a good use of the edge, it makes it more awkward to hold, and it really messes up most case protection. If they can make it with those edges, surely they could make it flat without needing large frames on the side.
128GB minimum or 64GB + SD. Pref 128 + SD. Bonus points for even more (my phone is CONSTANTLY full).
Whatever battery it takes to have the life a new Note 4 did (before updates and age lessened that) - an all day phone, with plenty of use.
Replaceable battery. I don't mind if it isn't convenient for mid day replacement, but I don't want the phone to just get continually worse with no way to recover battery life if I keep it for 2 years. I have liked the ability to yank the battery from a phone when it is frozen and will not shut down (and soft resets fail), but I've only needed that a few times... it could probably wait for home.
No glass back. Don't need to see family members continually finding new ways to crack parts of the phone that have no real reason for being glass, added to the complete inability to keep it looking remotely clean for more than the 2 seconds it takes to end up with hand prints all over the back.
As durable as possible with removable battery. Care more about drop/impact resistance and the screen than dust/liquid, but some liquid resistance is nice. Don't need it to be able to go underwater or anything - wouldn't trust that anyways.
Optional edge. I know; they like it being different... still don't see the point, other than making all the cases lousy.
Iris Scan
Hopefully good quality fingerprint scanner that is easily reached - up at the top may be too far on a Note.
Wish the antenna would allow voice/data simultaneously as they used to (<=Note3)
Less extra software, with hopefully faster android updates.
Not sure on numbers, but all for any improvement to the camera, especially in focus speed, clarity, resolution.
Wireless charging built in.
Good speakers are nice, but not important, I usually mute everything but calls and half the time those are going through some other speaker. Good quality mic that doesn't get too much background noise is a little more important.
More RAM. Whatever they put in, would probably like a little more.
If they were innovating software wise (not that I want bloatware, but occasionally they push something out that really integrates with the phone's hardware or unique features... my family loves their Samsung pay for having way too many cards at hand for every outdated little register that doesn't take Android Pay - they'll even ask cashiers to put it on the keyboard swipe strips), I'd like to see more happening in terms of integration with smart devices, wearables, and cars. I don't think they're really pushing in that direction though - have to hope for that from 3rd party apps. Maybe if their AI thing is really, really, really good about location aware activities and ease of use... but not expecting a ton there.
I'd also like it to be easier to partially unlock things, or temporarily turn off the screen lock - maybe even lock it to an app but leave the app running for a bit (for things you need to hand off to someone for any reason, or for something you want to run but need your hands off for a bit).
Improved dual tasking - in addition to two windows, perhaps a mode to keep both apps running as if they were foreground for fast swapping, or view a part of the app, etc.
Facebook
Twitter
Instagram