It'd be nice to see reputation updates in the app, as we get on both the desktop and mobile sites.
Mock-up of how this would look:
Other possible icon states:
While I understand reputation is shown in the feed, it's a bit unwieldy, and has no notification.
With this feature implemented, the feed could arguably lose both reputation and inbox items, and be left with the interesting questions that fill it up. This would make for a much more consistent UX across app and desktop.