If sea levels rose dramatically and some major storms damaged some dodgy reactors in south east asia?
We had that already: Fukushima. And the japanese don't usually build too dodgy. The Pakistani - Indian conflict going hot and ultimately nuclear is a dreaded only too realistic scenario even today and everything the devs said about the great mistake seriously hints at that.
If we are looking at the 21th century we can identify only too probable ressource shortfalls that will stop dead the most vulnerable countries / regions in their development, leading to the rise of extremist elements in mainstream politics. Take rampant water scarcity from aquifer overuse (leading to saltwater contamination in most coastal areas) ultimately leaving large swaths of agricultural land laying barren and the people that lived of it flocking to the cities looking for a living. At the same time, oil production can't keep up with demand and prices skyrocket, leaving developing countries unable to buy it in needed quantities. Fertilizer made from fossil fuels not only become very expensive, natural deposits of Phosphor run out too, leading to rising food prices, poor people would be unable to afford any more in a highly input dependant large scale agricultural infrastructure (due to previous land grabs in search for investment capital rent).
Nations scramble to build nuclear power plants, but they already know, that Uranium is going to become scarce only 20 years later. This would prompt existing superpowers and emerging ones to scramble for ressources much more agressively than today, leading to many conflicts.
A static and politically not fully integrated Europe would be unable to cope with scarcity induced continous recession, fueling internal nationalist tendencies and leading to the break up, or just the paralysis of the European Union, effectively removing it from the world map as a global player. The US would try to furthers its domestic ressource extraction programs, handing ever more power over to companies out of desperation, but even fracking, tar sands and huge subsidized mining operations would run dry after a short time, because technological innovation in extraction techs would fail to cope with demand. It would reduce its global military presence because of mounting pressure from its populace to cut the defense budget, gracefully stepping down from empire status.
China would not fill that gap and aside from some wars with its neighbors to grab convenient ressources (south chinese sea, Vietnam...) it would turn inwards. The collapse of demand for chinas goods on the international markets, leaves it with huge masses of urban population that would be unemployed and demanding better administration and a system with less built in corruption, blaming the party for the personal economic desaster they would be facing. This would prompt the party to step up internal security, effectively building up a police state.
Developing nations would face grim outlooks and a lack of positive perspectives for development which would lock them down in internal struggles over sellable ressources, bathing them in a wave of bloody ethnical and religious civil wars, leading to the rise of a multitude of warlords seeking to control the rent from ressource extraction. It would also reignite imperialist agendas, with all sorts of countries trying to get on the good side of these Warlords to gain extraction rights, but constant war would excerbate already existing ressource shortages.
In the developed countries economies based on ressource imports and goods exports (Europe, Japan, to some extent china) would collapse, creating an urban proletariat the likes of which have not been seen for hundreds of years leading to all kinds of problems, from nationalist to bolschewist revolutions, further removing them from the global pane and locking them in direct or indirect conflict with each other.
At the same time climate change would make large swaths of land become uninhabitable (droughts, flooding), uprooting communities and sending large masses of people on migrations to find shelter and the bare necessities for living. The global economy in its weakened state would be unable to finance even the most urgent mitigation efforts and mass migration would reignite old ethnic conflicts.
And then it gets really messy.
I didn't even get too much inspired by looking for a great mistake, thats just how i have seen the near future of mankind for years (worst case scenario though). So what IS the "great mistake"?
I dunno. Mass consumist based capitalism? Maybe?