We have a problem with search only indexing fields that have their "Field visibility and permissions" either set to be "Public" or "Custom" with the anonymous user able to view. Any field that is private or has some other custom setting isn't indexed.
I only use Drupal occasionally so I'm far from an expert but as far as I can tell reading around, search should index everything except if it's explicitly told not to.
I've searched around and can't find any setting that would seem to be causing it to behave in this way.
Have I misunderstood how it should behave or is there a setting somewhere I'm missing?
EDIT: I realise that I should have specified that the site is using the Field Permissions module to set the permissions on each of the fields.