Solved...
Instead of this:
$select = new Select(array('m' => 'menus'));
$select
->join(array('i' => 'menu_items'), 'i.menuId = m.id', $select::SQL_STAR, $select::JOIN_LEFT)->order('m.position');
$string = $select->getSqlString();
$resultSet = $adapter->query($string, $adapter::QUERY_MODE_EXECUTE);
I needed to do this:
$sql = new Sql($dbAdapter);
$select = new Select(array('i'=>'menu_items'));
$select->join(array('m'=>'menus'), 'm.id=i.menuId', array('name'), $select::JOIN_LEFT)->order('m.position asc, i.position asc');
$string = $sql->getSqlStringForSqlObject($select); // I get the string of the Sql, instead of the Select-instance
$resultSet = $dbAdapter->query($string, $dbAdapter::QUERY_MODE_EXECUTE);