Countries facing persistent demand shortfalls could learn a lot from Argentina's basically successful default and devaluation, but now, more than a decade later, the country is facing very different problems. Specifically, the inflation rate is high and rising, and the government is trying to constrain it with gimmicks that aren't going to work. The small gimmick of de facto price controls on Big Macs didn't work, and imposing de jure price controls on supermarkets isn't going to work either.
There are basically two ways you can reduce inflation. One is to implement tighter monetary policy to reduce the nominal growth rate of the economy. The other is to implement structural reforms that increase the productivity of your economy so that a larger share of nominal growth is real output and a smaller share is inflation. Argentina has a lot of inflation right now, so it probably needs some of both. Countries that get into inflationary spirals tend to struggle with them, since the political temptation to try to address it with gimmicks seems strong. That was the experience of the Nixon and Ford administrations in the United States, and it certainly seems to be the experience of the Kirchner administration in Argentina. But the evidence from the Volcker deflation in the United States and concurrent developments in Europe is that it isn't particularly difficult to implement a tighter money regime, you just need to decide you really want to do it.
For the developed world, I think the main lesson of Argentina should be that this is what a supply-constrained economy looks like. No country has optimal public policy, and today would be as good a day as any for America or any other country to implement policies that boost long-term growth potential. But a country whose primary immediate problem is on the supply side should look like Argentina, with high and rising inflation. Demand is chasing a fixed supply, so prices are accelerating. The USA since the crisis doesn't look like that at all—it's a place where both real output and the price level are below their pre-crisis trend because we have a demand shortfall.