The territories have not been spelled out in much more detail than that. In particular regarding the 2nd bullet of the quote, i.e. "any other area in Europe in which occupation forces of any of the Parties were stationed on the date when the Treaty entered into force", very little appears to have been written about it specifically, but it seems indeed it is obsolete according to one paper which explains its origin as:
A further element of the historical dating of Article 6 is the mention of
“occupation forces of any Party in Europe.” Now obsolete, this provision of
Article 6 was subject to a note during 1949 exploratory talks where it was noted
that for the purposes of Article 6 the British and American forces in the Free
Territory of Trieste as well as in Germany are understood to be occupation
forces. It was felt that an armed attack on the occupation forces should
accordingly be specifically mentioned.
That para cites two sources:
- John F. Hickman, North Atlantic Pact: The Drafting of the Treaty, PACT D-6/1, 20 (Mar. 29, 1949).
- Minutes of the Eighteenth Meeting of the Washington Exploratory Talks on Security, March 15, 1949 in FOREIGN RELATIONS OF THE UNITED STATES, 1949, WESTERN EUROPE , IV, OFFICE OF THE HISTORIAN 213, 223 (1974).
So, yes, it was understood to cover areas of Germany (which was not founding member) and a small portion of the Adriatic coast, which was later partitioned between Italy, Slovenia, and Croatia.
However, all of these countries are full NATO members now. Although the last two of these were part of Yugoslavia which was more aligned with the Soviet Union (although not quite a member of the Warsaw Pact), there was apparently no discussion to make some clarification in that regard during the cold war.
The text you've quoted actually includes the modifications done with the accession of Turkey, which was specifically included in the article 6 text then (via the accession Protocol). When, in 1963, France recognized Algeria's independence, it was not felt necessary to remove the text regarding the "Algerian Departments of France", but a communiqué was issued by the North Atlantic Council on Jan. 16, 1963 that
The Council noted that insofar as the former Algerian Departments of France are concerned, the relevant clauses of this Treaty had become inapplicable as from 3rd July, 1962.
Also, when other European countries acceded later, no text modifications were done to the core articles (unlike in the case of Turkey), i.e. the extension of territories covered was left implicit thereafter.
As to the ambiguities like the "North Atlantic area", which appears several times in the treaty, some US Congress notes indicate that was deliberate:
the word area is to be understood to cover
the general region rather than merely the North Atlantic Ocean in a narrow sense.
This is also confirmed in the 1949 Executive Report on the North Atlantic Treaty
produced by the U.S. Senate Committee on Foreign Relations. In it, the U.S.
Senate stressed that “[i]n view of the purpose of the treaty to deter armed attack,
the area covered by the treaty was deliberately described in general terms rather
than defined by the lines of a map.”
EXEC. REP. NO. 8 OF THE COMM. ON FOREIGN REL. ON THE NORTH ATLANTIC TREATY (1949), at 15.
It's perhaps worth nothing in this context that the 1947 Treaty of Rio did specifically include the North Pole as the northernmost point, but this doesn't appear explicitly in the NATO treaty. And there are seemingly no drafting notes for the latter where specifying a northern boundary was even discussed. This is quite in contrast to the southern limit, clearly specified as the Tropic of Cancer in the treaty itself.
There were apparently NATO discussions during the 1963 Cuban [missile] crisis, but the meeting of those notes were insofar not made public, only a letter from the Secretary General of the Western European Union (addressed to NATO) requesting discussions.
As you probably know, the NATO treaty was not invoked during the Falklands war; the area of contention was in the South Atlantic. The US did provide the UK some behind the scenes assistance and seemingly was prepared to do much more like quickly replace aircraft carriers the UK might have lost.
Other areas nominally not included in the NATO treaty for the same reasons are French Guiana and (the US state of) Hawaii; the last one was discussed in a State Department memo in 1965.