Customer places an order, and from the customer side all seems to go ok, except the customer cannot see the order in order history. In admin the order does not show up, unless it is searched for. The field 'ot_total' is not added to the database table 'orders_total'.
If this field is entered manually then the order shows up as normal, in admin and customer history.
The cure is to check the sort order of 'total' in 'admin-modules-order total' and make sure it is unique, ideally set at 999 (as per Michael Sasek suggestion), and manually enter the 'ot_total' fields in the database to correct existing errors.