PSN Improvements
Better/more CDN's with universally consistent speeds that are competitive with Live/Steam/Origin...etc
Free, unlimited (or at least significantly increased in size) cloud storage for saves, as well as a family account feature set for saves (no need for sub accounts), auto-sync save files as they are modified
Username changing along with a username history system in the user's profile page
Behind the scenes (less disruptive) maintenance
Cloud storage for screenshots, especially trophy screenshots (maybe recordings too if 30 sec or less?)
PS Store Improvements
Fix bug that prevents users from accessing the Store in certain situations, needing a reboot
Up-to-date digital titles (fully patched when downloading post-launch)
Store wishlist, gifting system (cross-region gifting?)
Correctly tagged games in the store
Refined Store navigation, design, fluidity/polish and organization
Refund system similar to Steam's
Enhanced Store game pages, include user reviews, make screenshots/videos standard for all titles
Purchase and management of PS Vita downloads through the PS4 Store
Account/Profile Improvements
Continuous trophy syncing
Online/offline status
Better friends list functionality with nicknames, grouping by categories (games, relationship), and VIP tags tied to the notification system
Enhanced user profile page showing favorite games, screenshots/recordings, game wishlist, deeper activity sections (game statistics)
Account region change
Deeper social integration (G+, Facebook, Twitter...etc)
Viewing friends' online statuses across PS3, PS4, and PSV
Security Improvements
Two-factor authentication
Improved account recovery process
General usability Improvements
Search function, better organization and filters for download history/library
Universal game invites
Direct developer/players interaction, statuses, in the game hubs
Custom avatars (purchasable or own uploaded via PS app)
Refined activity feed (What's On section), fix a bug where playing a game post-patch showing as if it was the first time you've played it
Share notification for recordings/broadcasts
Message system refinement
Would love these and a lot of the other suggestions, especially the online/offline status. Something Shu promoted/stated before the ps4 launched ffs.