Search builder 'forgets' operator when retrieved via Manage Groups

CiviCRM 3.1.3. Reproduced on drupal.demo.civicrm.org

Two bugs have been found in Search Builder:

1) Clicking on "Another search field" correctly adds a new search fieldset, but, incorrectly re-directs the user to the wrong page. This is not a serious issue, but, is an annoyance.
2) Creating or editing a Search Builder query and then later retrieving the Search Builder query via Manage Groups results in the 'Operator' being lost when the 'Operator' is 'IS NULL' or 'IS NOT NULL'.

A screen recording is attached which documents the steps used to re-create these issues on demo.

Use case: A complex query is required to extract users to whom postal mailings will be sent. The only tool available to end users capable of creating these complex queries is Search Builder. Often a more technically advanced end user will create the Search Builder query to be retrieved and used by a less sophisticated end user. With the existance of the bug, the query cannot be passed-on to a less sophisticated user to run.

Alternatives: If Search Builder cannot be used, a programmer will need to be engaged to write the required queries (cost prohibitive for many organizations) or a non-CiviCRM solution will need to be found.