I know that all entities need a dc to be produced. I also know that the faction with the dc is listed underneath in the rules page. My question is who can produce entities that are not rare or unique, but have no faction listed as owning the dc. By entity i mean ships, vehicles and items.
The only forces that influence a course of action are will, luck and chaos
I don't know of any ships that have no DC owner that aren't rare, but if they exist then most likely what has happened (and the same with vehicles and items) is that the faction that had the DC has dissolved, taking the DC along with it. In that case, no one will be able to produce it until R&D is released, and it is researched again by someone else.
And Mikel there are ships like that - the last generation of CP ships. They haven't been listed as rare, btu they are also non-producable.
So to answer you question, for anything that isn't a facility/station and has no faction listed under it, it cannot be produced at this stage. For facilities/stations, there are several that have no faction listed since anyone can build them (Eg Space Colonies, Hotels, Power Generators). However there are a few facilities (or at least there were) that have no faction listed, yet cannot be built by anyone.
Facilities usually do not have faction listed, as no datacards exist for them (except for HQ facilities at some times). To find out what factions can produce what facilities, check the Faction Creation page.