Right now, activities window is more like a leftover of the old firefox download window, a relic from the past. Let's change this for a more useful tab.
I was thinking about a "sync status center" where you can check in a table the status of: column1: all mail accounts: one account per line column2: all other sync statuses (calendars/tasks/caldav, ical, contacts/carddav, IM, etc.)
with on each, last successful sync date/time and sync status (failed:red/syncing:blue/OK:green), and maybe a button to force sync a specific account
maybe something like this (crude edited screenshot):