The calendar should have the option to hide user groups' birthdays (and events) from the calendar. For example, a banned member's birthday should not be displayed.
I'd be happy if it simply honored the "don't show in the directory" group setting, but it would be better if there was a multi-select box in the calendar display birthdays settings where you could select the groups whose birthdays you wanted to hide (or show). If a banned member had scheduled an event, there should be the option to hide that as well.
For completely private boards where only registered users can see content and registrations are turned off:
The create account button be hidden if board registrations have been turned off.
There should be an option to selectively have the board only display the login screen for anyone who is not logged in, hiding everything else. (Ideally this would have bunch of checkboxes for all the home page areas, so you could selectively disable/enable them.)