Minor gripe, but... can we please be allowed to change the notification settings on the Android app?
I personally don't need my phone to vibrate and ring. And I don't want the sound to be the default; I want customization!
Implemented as of version 0.1.66 coming out tonight!
Edit: The remaining part of this as explained above is now implemented
I concur that the notifications can be super-annoying and not having control over them is a design flaw.
As mentioned in the comments, it's possible to disable notifications specifically for an app. Here's how to do it for most devices I've seen, with recent enough Android version:
Open App Info, e.g. Settings -> Application manager -> Downloaded -> Stack Exchange
Uncheck "Show notifications"