TLDR: Mobile is sad. Can we have web push notifications?
(While the eventual intended audience will know what I'm talking about,google has a nice, though somewhat technical article on what this is. I don't expect it to happen soon, but would be nice to put it on the radar.)
For starters - and this could take the proverbial 6-8 weeks or more, could we have web notifications on the mobile/grand unified responsive design pages? This would help do notifications for both desktop and android (apparently ios dosen't do webworkers/notifications correctly yet - but whatever work's done would be useful even after that). I'm not sure what else that the mobile apps offer but this is the one thing I'd miss. Its definitely not a high priority but something I'd like to put on the radar
Considering that there's plans to unify the mobile and desktop views, this might work for both.
The mobile applications are something that power users of Stack Exchange love. That said, they kind of have been left stagnant a while - and they're essentially technical debt, especially with, well, the mobile landscape changing a fair bit. Might be worth planning for the time they are no longer around.