The biggest butterflies from this come after the end of WW2. Truman made a number of absolutely critical decisions that shaped the world for the next 50 years and beyond. I find it hard to imagine that the world would be exactly the same if he hadn't been President. The bombing of Japan, the UN, the Berlin Airlift, the Marshall Plan, NATO, containment, Korea, etc. all were the foundations of the West's approach to Communism until the end of the Soviet Union and NATO remains as the key policy with respect to the defense of Europe. None of these decisions was easy and all could have turned out differently. Truman certainly wasn't perfect, but he did have a knack for getting the big things right, IMO.
Lloyd Stark as VP in 1944 is certainly possible. Good catch there by David T.