Adding validator to a number of fields
You'll need to add a hook_form_alter(), check the form ID matches one of those that you're interested in, then add a validation handler to the form. The validation handler will perform your validation against the form fields. Something like

function MYMODULE_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  $form_ids = array(
    'article_node_form',
    'page_node_form'
  );

  if (in_array($form_id, $form_ids)) {
    $form['#validate'][] = 'MYMODULE_field_validate_callback';
  }
}

function MYMODULE_field_validate_callback($form, &amp;$form_state) {
  if (empty($form_state['values']['field_x'][LANGUAGE_NONE][0]['value'])) {
    form_set_error('', 'Field X cannot be empty.');
  }
}


I don't know of another way to do this as hook_field_validate() is only called for the module that implements the field type.