I have revisited this as after a re-read it seemed a little on the scrappy side. 
From my ‘fresh-eyes’ test I have discovered that:
- 
Setting the Moderator inbox to ‘Watching’ (and the mod’s PM email user preference to ‘always’) you will immediately get a notification alongside the red Review Queue one, and an email sent out, but only for the something else flags. The others will not generate a message in the Moderator’s inbox, so won’t trigger any inbox notifications. 
- 
But if you also set notify about flags afterto the minimum of 1 hour rather than the default 48 then that will send out a PM to the Moderator inbox, which will trigger a notification and then an email.
- There is also the notify about queued posts afteradmin setting, which is only concerned with those posts which require approval.
- And a similar one pending users reminder delay minutesfor users needing approval
Hopefully that is a little clearer. 