The easiest to distinguish are direct objects that begin with an article:
|They broadcast the controversial documentery last night.
Having a definite article, de omstreden documentaire (the controversial documentary) is a specific direct object, and is thus placed at the beginning of the middle part. Among all controversial documentaries, it is this specific one that was broadcast. Although it is more common to place a specific direct object at the beginning, it is also allowed at the end: "Ze hebben gisteren de omstreden documentaire uitgezonden".
If we replace the definite article de (the) by the indefinite article een (a), we HAVE TO move the direct object to the end of the middle part:
|They broadcast a controversial documentery last night.
The indefinite article makes the object non-specific. This phrase does not refer to a specific documentary, but to any controversial documentary.
|They broadcast controversial documenteries last night.
Omstreden documentaires is a non-specific direct object. Just like in English, the plural indefinite article does not exist in Dutch. A plural indefinite noun simply gets no article at all.