that notorious hostile article about the Faroes

Here I would translate a little freely, as the Danish is dated.

I would probably leave out snart = soon.

"Ja, det ved snart alle" is an expression still in common use
- (Practically/just about) everybody knows that!
It is emphatic in Danish, but can have the opposite (qualifying) effect if translated into English.

Produkt
I would take this as the second meaning defined in Nudansk Ordbog:
1. en fremstillet vare ...

-- et resultat af et arbejde, en indsats el. en udvikling ¯ produktet af en indsats · hun er et produkt af sin tid

i.e. the result of a journalists's work in the other newspaper.
That to distance the present writer from it, since he wants nothing to do with it.

Hope that helps!