Hello Klas
Thanks For your answer. Let me please present my difficulties with free object reordering on a "currency content type".
This is a structure of the DB table
#__obch_mena (currency).

Here you can see the records

This is the list view of my search type for administration of currencies. The id and ordering fields have jGrid typography

This is the Order by configuration

This is the storrage of mena_id field...

..and his is the storrage of mena_ordering field

The reordeing is actually enabled on the page..

..but the AJAX order save returns this error and the ordering is not stored

Eventually, I added the CCK ID field to my List View (right at the bottom)

After adding the CCK ID field, it's not dispayed at the seb_table template at all. With nor without the jGrid checkbox typography. That's really strange
The AJAX save order does't return any error but the ordering is not stored in the database so after refresh, the reordering is gone. Also the notice please that the POST parameters have changed.

Would you please look at this and kindly try to suggest what am I doing wrong? If this works, it would be really amazing feature especially for such as small non-article objects e.g. currency
Thanks so much
Michal