I disagree with the comment that it was pointless. These islands, inhabited only by British subjects, were wrongfully taken. A corrupt government was humbled and forced to give up power. Britain proved again the valor and skill of its royal marines, SAS, and other units mentioned in this article.
Why was it pointless ?
Pointless from the Argentinian point of view!?. As you said, Britain gained military prestige and experience and showed its enemies around the world that it would fight, even for a desolate island full of sheep. Plus there is rumoured to be vast reserves of oil under the south Atlantic that Britain can lay claim to as they are within the territorial waters of the Falklands. Apparently the oil is not ready to pump out just yet but the government has been borrowing against it anyway. I cannot confirm this at all, just something a friend told me, could be another crackpot conspiracy for all I know.
Ultimately all war is pointless. I remember a girl back in my schooldays suggesting that disputes should be settled with a computer game war. We laughed at the time but now I think it makes a lot of sense! Civilization played for real, nerds become warriors Maybe mankind needs to settle its differences by actually killing one another. That's the way it has been for the entire history of Civilization and it does not look like drawing to an end anytime soon.