With a POD in 1930, and culminating in a February 2009 newspaper article titled 'End of War; End of History?' that declares an end to the 'Tragedy of the Commons' and a new age peace for the citizens of the 'world government.' What are some of the more realistic possibilities of this happening (through the USSR, Third Reich, Japanese Empire, US, British Empire or some other unknown)? What would some of the policies of such a government be like? What would be the implications for the future?
Someone saves Edith Keeler's life.

(I think they went back to 1930 in "City on the Edge of Forever." Of course, maybe that's where you got the year to begin with.)
Hmmm, who is a world leader who would be willing to give the League of Nations some teeth? Let's say they intervene agaisnt Mussolini in Italy and stop him in Ethiopia, Hitler is killed in 1938, and they also stop Stalin in Finland. The Japan/China war will still happen, but as the League becomes stronger, it's more of a mandate; then the U.S. finally joins in after the attack on Pearl Harbor.
By the '80s or so, you might see the German and Soviet governments topple, if not before for Germany, and they become the last holdouts, as the LoN has basically become the global policemean.
Of course, nations actually giving up sovergnty is a toughie, but maybe it can be sort of like a United States of Earth. So, each country can do things within their borders just like states can int he U.S..