Here is the code that the error messages in the first post refer to, with offending lines in bold:

/**
       * Real escape, using mysql_real_escape_string() or addslashes()
       *
       * @see mysql_real_escape_string()
       * @see addslashes()
       * @since 2.8.0
       * @access private
       *
       * @param  string $string to escape
       * @return string escaped
       */
      function _real_escape( $string ) {
            if ( $this->dbh && $this->real_escape )
                  return mysql_real_escape_string( $string, $this->dbh );
            else
                  return addslashes( $string );
      }

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/**
       * Escapes content by reference for insertion into the database, for security
       *
       * @uses wpdb::_real_escape()
       * @since 2.3.0
       * @param string $string to escape
       * @return void
       */
      function escape_by_ref( &$string ) {
            $string = $this->_real_escape( $string );
      }