Address disappear from profile when Address Book is turned on.

The test for the 'view' is not what I would expect.

If I look at someone else's profile, that test will prevent me from seeing his/her profile if I also have 'Address Book' turned on.

I suggest you remove the test of the variable addresses_user_book. (I show it commented out below).

The correct test could be quite complex, and there is not reason to not show the currently logged in user how other users will see his/her profile! (Well... otherwise, if the addresses book is turned on, the feature of showing a user his/her address is automatically turned off which seems to be broken. We could however, have another flag to say whether the user addresses are visible or not in the user profiles.)

// in addresses/addresses_user/addresses_user.module, last function.
/**
 * Implementation of hook_user().
 */
function addresses_user_user($op, &$edit, &$user) {
  if ($op == 'delete') {
    module_load_include('inc', 'addresses_user');
    _addresses_user_address_delete($user->uid, 'user');
  }
  elseif ($op == 'view' /*and !variable_get('addresses_user_book', FALSE)*/) {
    module_load_include('inc', 'addresses_user');
    $addresses = _addresses_user_address_get($user->uid, 'user');
    $address = $addresses[0];
    $user->content['addresses'][] =  array(
      '#type' => 'user_profile_item',
      '#title' => t('Address'),
      '#value' => theme('addresses', $address),
    );
  }
}