(A very small detail only :-)

I like the iPhone app, where you can set the app's badge to show the number of unprocessed items in the inbox. This is very useful (easy to miss new emails otherwise).

Would it be possible to have that in the other apps, too, e.g. the web app? (As it is now there is constantly a red mark on the browser tab icon, because there are usually items in the Today list, and this means you do not notice that new things have arrived.)