When you are eliminated or surrender from game remove the chat notifications
Whenever I surrender or get eliminated from a game my dashboard is still filled with chat notifications even though I am no longer in the game. So much that sometimes I have to sort through 90% of games Im not in to find the chat for games that I am in. Eliminating the chat notification for games you are no longer in will help clear up the dashboard and make it easier to see chat notifications for games you are actually in.
Just set the filter to 'Active games where I am not eliminated.' You won't have these games show up on the dashboard anymore.
^ I think this should be true for games where you get removed by the host before the game starts