I’d like to see something for mobile where a ‘widget’ could be added to our homescreen to view select games in progress. Even just a ‘view-only’ type function would be neat, where the game could be observed, but maybe clicked on and directs us to the game in a browser.
I’d probably dedicate a whole section of one of my screens on my tablet to games in progress/being observed. 
Anything like that out there?
I’m not sure if there’s an official OGS app although I think there are some clients out there. I’d be happy with a simple number at the app icon to see with a simple glance if there are any games pending me to play, much like when you get a message, but a full widget would be very nice to see too.
I don’t know if such a screen widget already exists. However, it should be feasible and pretty easy to build.
Pulling the SGF of any game is straightforward via the API. A widget would just need to parse the file and render the board position of the last move, plus some UI for entering the game ID.