How do I clear completed tasks from the view in Palm Desktop? I know I
can switch to Tasks view and delete each one, but I'd like to stay in
the Date Book screen and have them automatically remove them from view
when I check them as completed.

Go to the To Do List screen, click tools, preferences.  UnCheck the
the show completed items box.  Now when you check off an item it will
go away.  This setting will carry over into the to do view in the date
book.