Hardly any difference with a normal Saturday. I don't know the working hours of the Banco Nación at EZE (I think they work 24/7 but don't quote me on that) but banks in downtown Buenos Aires will obviously be closed. Shopping malls will be open, and so will be restaurants/cafés. I would check on museums, not really sure about that, though I'd like to think the Museo Malvinas will be open!

Other than that, there might be a peaceful demonstration somewhere in town (small groups sometimes gather in front of the British Embassy in Recoleta), but nothing to worry about. Usually in Malvinas Day all the action moves to Tierra del Fuego - many veterans down there and fueguinos still get very emotional about the war.