Since Article 5 of NATO wasn't activated when Argentina invaded the Falkland islands, did the Soviet Union use this to prove that the West was weak and to bolster its own reputation?
I found an article in Soviet journal Foreign military review published after two years of Falklands War called Some results of Falklands’ Conflict (Foreign military review, 1984, Issue 5, p. 9-17).
There is an excerpt: “Western military experts consider armed conflict between two countries as local war with the participation of different kinds of military forces with the defining role of the navy. Its particularity they see in the following: no side declared condition of war with enemy. Military operations were constrained both in composition of participants and coverage of territories; there was no threat to the population of countries participating in the conflict; both sides did not have an aim to change the political status of opposing country.”
This piece presented without refutation, so this view is shared by authors of the article (captain of second rank Yu. Marov and captain of third rank A. Biryusov). Didn’t find any mockery of NATO inaction. So, this conflict in this article regarded as local conflict that doesn’t infer necessary NATO action.
The Soviet Union never used this as a an argument because Article 5 wasn't applicable to the war as the Falkland Islands weren't covered by the treaty. The text of article 5 is as follows;
“The Parties agree that an armed attack against one or more of them in Europe or North America shall be considered an attack against them all and consequently they agree that, if such an armed attack occurs, each of them, in exercise of the right of individual or collective self-defence recognized by Article 51 of the Charter of the United Nations, will assist the Party or Parties so attacked by taking forthwith, individually and in concert with the other Parties, such action as it deems necessary, including the use of armed force, to restore and maintain the security of the North Atlantic area.
Any such armed attack and all measures taken as a result thereof shall immediately be reported to the Security Council. Such measures shall be terminated when the Security Council has taken the measures necessary to restore and maintain international peace and security.”
As you can see it only covers Europe and North America, which doesn't include the Falklands. This was by design as the US didn't want to be on the hook for defending European colonial empires.