It'd be great to be able to define what shows up on my Notifications sidebar: which game's comments, which game's moves, if my own moves/comments show up or not.

Also, the option to have notifications for your Favorites. Like, I'd love to be able to get a Notification on my sidebar if one of my Favorite players creates a new game so I don't have to scroll around in my super unorganized Favorites page. But you should be able to turn it on and off so people can choose how much spam or not their sidebar gets.