I think now more than ever is the time to have a phone that is as reliable as the iPhone. Fast, stable and FAST.
1. Solid 60fps when navigating the UI. If every iPhone for the past half-decade has been able to do it then there's no reason a state of the art Nexus with the latest software can't. The 6P is not there yet but it's close.
2. Fast storage. App loading and install times as well as camera performance are heavily dependent on having fast storage. Fast SSD quality storage will do wonders. Just look at the iPhone 6S.
Fast storage will improve HDR+ processing time.
3. Camera improvements:
3.1 A camera app which doesn't blow a**. HDR+ is fantastic but it's a shame it's attached to a trash camera app that doesn't even allow for simple manual exposure controls. This NEEDS to be fixed.
It would also benefit from a UI overhaul.
3.2 Larger sensor and/or aperture and a longer effective focal length. 35mm would be great. I know this isn't easy but it's not impossible.
3.3 Dual Pixel autofocus. Look at how amazing the autofocus on the GS7 is. Just copy it if need be.
3.4 Image stabilisation in 4K.
4. Power efficiency. A new phone doesn't need to have a bigger battery than what's on the 6P in order to get fantastic battery life. If the components like the display and WiFi/LTE/GPS radios are power efficient then we should be set for getting 5 hours SOT easily.
5. Waterproofing.
6. Good speakers.
7. Good thermal management. A copper pipe like on the Lumia phones to spread the heat more evenly around the device will avoid a noticeable concentration of heat around the area of the SOC.