You could have PODs of either the rain holding off, denying the Germans the advantage their boots and their wet-weather training had given them, or have Puskas' 89th minute goal ruled onside, or a penalty awarded for Sandor Kocsis in the final minute, with the penalty being scored and the game going in to extra-time. If extra-time was drawn, with no penalties to decide the match, there would be a replay two days later - which Hungary should win.
As for the aftermath:
- Adidas boots take longer to take off, and perhaps are less able to initially outstrip Puma and other boot manufacturers.
- Hungarian Revolution doesn't occur in 1956 as the Communist Party is able to draw upon the satisfaction created by World Cup victory.
- Germany follow their defeat in 1954 with fourth place in 1958 and (let's say) second in 1962 (to Brazil) - by the time 1966 comes around Germany are either more determined than ever, and triumph 3-1 over England in the final, or 'recognise' themselves as perennial nearly-men, losing to the Soviet Union in the semi-finals 1-0, setting up an England - Soviet Union final (which England probably lose). By 1974, despite having one of the best German teams ever, demoralisation plus a recognition that communist countries are best at football causes Germany to lose in the semi-finals to Poland - the Dutch winning the final with their Total Football.
- This defeat, coupled with an economic decline in Poland leads to a Polish uprising in 1976, crushed by Soviet military intervention, with assistance from East Germany and Czechoslovakia. The Archbishop of Krakow, a Karol Wojtyla is shot, causing an international incident between the Soviet Union and the Vatican City. Tensions within Hungary finally bubble over. The combination of these events in Europe prevent Soviet intervention in Afghanistan, which falls in to a state of anarchy, with fighting between a stubborn communist government and Islamic mujahideen.
- In 1978 Giovanni Benelli is elected Pope, becoming Pope John Paul II in honour of his predecessor, until his death in 1982.
- Italy win the 1978 World Cup, beating Argentina in the final, causing rioting, bringing down the military junta.
Or maybe not!