The Great Mistake

First off the great mistake was made to be a ambiguous thing ,the idea is up to you to decide what it was, but still the devs of civilization beyond earth tried to explain a bit of it when they were making the concept for the game.

The Inflection point : is a mathematical theory that basically describes a limited amount of resources ,that will make space travel in the future impossible because of the lack of available materials to go out of Earth , for example the quantity of oil on Earth is limited and will be gone some time in the future (the theory describes with some accuracy when this will happen).

Nuclear Incursion: China starts a nuclear war in some Asian countries , as a result many parts of those countries are evacuated creating a mass migration and helping to re-shape the geopolitical landscape of the world in a small time frame.

Global Warming: the fast raising of the sea level was making the mass migration of many countries even more intense, blending many cultures and diferente people together ,some of those with little to no contact before the mass migration.

Combining those events and everything that might have happen in the course of that time, this would have made the Great Mistake concept created to be used in Civilization Beyond Earth