Originally Posted by
waldronate
The biggest single problem with a flat world is that nothing that we take for granted in our spherical world works. There is no day/night cycle. There is no heat transfer because there isn't differential heating by latitude. Similarly, ocean currents don't work. If you insert a day/night cycle through some continuously-maintained mechanism, what do you do about moons/planets/stars in the sky?
Let's consider a flat world that's ten thousand miles across. What happens at the edges of this world? If we want to go classic discworld style (waterfalls at the edge, some elephants, a turtle, the whole bit), we can put a big and hot ball that rotates around the world to give something that looks like a sun. I have no idea how an atmosphere would be retained in such a case, though, unless maybe gravity would be linear "down" rather than towards the nearest mass. A many-kilometer-high wall at the edge of the world would keep in the ocean and the air, but weather doesn't work anything at all like on Earth under those circumstances. If you want Earthlike behavior, then you'll need some consciousness that is responsible for ensuring that each aspect (air currents, heat distribution, ocean currents, and so on) gives a reasonable simulation on your flat space.
If you're going with a flat world that has diffuse edge conditions (warping off to different "realms"), then you can fudge those edge conditions to give you something that's vaguely Earthlike, but there's still the problem with astronomical things.
The traditional approach to this situation is to treat everything as Earthlike, add magic and gods suitable to your own tastes, and ignore any logical inconsistencies that arise.