I have just set up MobileOrg to work with my new iPhone, and have the
  following problem: I can view the contents of my various .org files,
  but "Agenda Views" appears to be empty.  I have the weekly agenda view
  open when I push the .org files to Dropbox.  I am afraid I am missing
  something very basic, but can't for the life of me figure out what it
  is!

Are you using "org-mobile-push"?  That creates "agendas.org" and puts it
on the server.  You should look in your webdav space and see if it is
there and sensible.  My agendas.org file is 150KB and starts

#+BEGIN_SRC org
#+READONLY
* Week-agenda (W10-W11):<after>KEYS=a TITLE: Agenda </after>
** Tuesday     8 March 2011
***  TODO [#A] a task
#+END_SRC org