Trying to get external cron working
After lots of messing around, I upgraded to 4.6.8 and then made a clean copy of the latest civicrm 4.6.8 files into the civicrm/CRM subdirectory, and the cron job ran properly. However, my Wordpress installation failed, because there are multiple Wordpress installations on the server and a search from the top root caused basedir restriction errors (and would probably have failed for that reason...).

The fix was to add the following lines to civicrm.settings.php, just before the section "do not add anything below this":

if (!defined('CIVICRM_CMSDIR')) {
  define( 'CIVICRM_CMSDIR', '/nhldata/631/106631/data/web/predigerforum/htdocs/wordpress/' );
}

It was important to include the "/wordpress/" at the end!

I'm not sure that this overriding parameter is really documented, though. I found it referred to in a forum post.