Envision a world where by 1939, both the Weimar Republic and the Russian Republic (a.k.a. the Provisional Government) have survived, and not only that, Taisho Democracy is preserved in Japan while a succession of progressive presidents in the U.S. manages to head off the Depression before it can happen - instead, there's a contained recession in the mid-to-late 1920's. The only major rogue state anyone can remember is Fascist Italy, which was recently overthrown by an international coalition after it invaded Abyssinia.
By 1939, Mussolini is awaiting trial at the Hague, negotiations for a 'European Economic & Industrial Association' are being held in Vienna and in the States, presidential candidate Wendell Wilkie is running on a pledge to bring the United States into the League of Nations. The biggest sore spot in this burgeoning liberal democratic world order is an increasingly instable China that acts as a temptation for the radical militarists in Japan. There is also a growing nationalist consciousness spreading in the colonized parts of the world, split between those that follow the non-violent ways of the Indian independence movement and the revolutionary guerilla tactics of the Vietminh - however, these have not yet grown into global crises of the first order. Squabbling between Jews and Arabs in the Holy Land is another sticking point but the British seem to be doing a good job of keeping a modicum of stability.
Overall, the world seems to be enjoying a period of durable peace and the first pangs of an economic boom managed by a concord of friendly, democratic great powers, so much so that American journalist Walter Lippmann writes a piece entitled 'The End of History and the Coming of the World Citizen.'
"What we may be witnessing is not just the end of the vicious, imperialist rivalries that fueled the fires of the Great War or the suppression of the insurrectionary ideologies - Bolshevism, Fascism, Anarchism - that sought to remake the world in their own terrifying image, but the end of history as such: that is, the end point of mankind's ideological evolution and the universalization of Western liberal democracy as the final form of human government [...]
"As we look upon the globe, countries are turning to freedom, economic and political, and are leaving behind the collectivist-jingoist instincts of the past. For them, the great discovery of the 1930's has been that, lo and behold, the moral way of government is the practical way of government: Democracy, the profoundly good, is also the profoundly productive.
"To the great mass of people in the world today, there is no alternative."
Snapshots of World Leaders
The United States - President Charles G. Dawes - nearing the end of his two terms; respected statesman celebrated for maintaining peace & stability at home and abroad; fiscally conservative Republican but surrounded by progressive Keynesian advisers, managed a budget surplus in his last two years; sent the American Expeditionary Force to aid in the League of Nation's Italian intervention
Great Britain - Prime Minister Neville Chamberlain - immensely popular reformist Prime Minister overseeing the finishing touches of his radical programme, the Great Housing Bill of 1939; his most immediate political challenge is not so much the weakened Labour opposition as it is the hard right faction of his own Conservative Party led by the flamboyant reactionary Winston Churchill
France - President Albert Lebrun & Prime Minister Edouard Daladier - in charge of a centre-left coalition government implementing social and economic reforms; trying to out-compete the Germans in a friendly contest of 'who can build the best welfare state?'
Germany - President Otto Braun & Chancellor Kurt Schumacher - overseeing German economic recovery and integration into the emerging global and European multilateral orders
Russia - President Pyotr Krasnov & Prime Minister Alexandr Antonov - the partnership between a right-wing monarchist ex-warlord as head of state and a crusading socialist revolutionary premier as head of government has turned out to be surprisingly productive, managing to stabilize the rapidly industrializing Russian economy while also finishing off the last remnants of the Bolshevik insurgency in the Urals
Japan - Prime Minister Wakatsuki Reijiro - aged, long-serving liberal Prime Minister whose most urgent task is the placation of the vocal militarist faction within Japan's leadership; interested in cementing both the electoral supremacy of his Minseito party and the constitutional parliamentary system in which it operates; has articulated a vision of a peaceful, pan-Asian future built on colonial emancipation, cooperation and democracy as an alternative to the militarist's plans for regional domination
China - President & Generalissimo Chiang Kai-Shek - the troubled strongman leader of the only major country that does not seem to be doing well, where the central government is fracturing under the weight of rampant political corruption and economic mismanagement, rival warlords and red guerillas, starvation in the country and unrest in the cities, the re-penetration of foreign imperial influences - most particularly, Japan
In terms of filling in the rest of this world on a more detailed level and projecting its future, I guess the question would be, what could go wrong?