This has already been covered at length by the members above. I thought I'd make a few slightly different comments though. The Earth being flat causes so many problems. What's a lunar eclipse? Why can we see sunlight from the moon at night but not sunlight from the sun? Why is australia the wrong size. Why can we fly south from chile to australia? Why do sunrise sunset times exist the way they do at every city south of the equator? Why does gravity not behave radially? Why can we see stars? Does the universe exist outside of the flat earth? or does it start at the edge of antarctica? If there's a universe dome, what happens when you bump into it? If not, what happens when you jump off the edge of antarctica? Why do weather patters act as though the earth is round? Why is it possible for a cloud to exist spanning the south pole? How does the south pole exist?
We'd need a new theory of gravity, a new process for ocean currents, weather, tides, the earth's magnetic field, solar radiation, satellite orbits, formation of the earth, age of the earth, fossil record dating, evolution. We'd need to understand what keeps mars orbiting? Certainly not the sun. All of geology is ruined. All of celestial mechanics is ruined. Newtonian motion is ruined. Magnetism is ruined, and that affects our understanding of electricity.
You're talking about nothing less than the complete and utter destruction of almost all human knowledge of the physical world. It affects how computers work, how cars work, basic mechanical advantage. If you're talking about overturning Newton, Einstein, Maxwell and all of the rest of them (which you pretty much have to be), we can't even understand why the cross beam over your head is capable of bearing the load of the roof.
So it's kinda hard to imagine this scenario.