What determines the legitimacy of government's actions?

That can be answered a few ways. In a democracy it is the people, indirectly, who determine the legitimacy of the government. In the US it is the supreme court that determines the constitutionality of laws enacted by congress. In other countries they have courts and oversight committees or government bodies that determine the legitimacy of the acts of the other government branches. In dictatorial countries it is the government itself that determines whether or not what it does is legal,( obviously it never decides against itself).

On the world stage there are several groups supported by the majority of countries that determine the legitimacy of other countries actions. The World Trade Organization, The World Court, NATO, OAS and the United Nations among others also have means of determining legitimate acts of other nations.