I'd add historical control of the territory. Which again... the modern nation of Argentina has never had any long period of peacetime control of the Falklands.
I guess you could add a fourth and weakest, being 'the desire of a government not in control of the territory' and you'd have almost all claims covered off.
Maybe I should have my coffee first next time...
1) Actual control of the territory
2) International recognition
3) Desire of the people in the territory
In regards to the Falklands, Argentina has none of the three. It is possibly the weakest claim to a territory that is commonly mentioned on JetPunk.