Alright, let's get this straight. The Earth is a flat disk, North Pole at the center, with the sun at moon more or less above the equator, moving North and South with the seasons and traveling East to West around the entire globe once per day. Pretty decent model that explains the days and seasons.
Now, let's include the facts.
Phases of the moon. The half moon is easy to demonstrate (moon and sun about same altitude), as are the 3/4 moons (sun lower than the moon), and crescent moons (sun higher than the moon). However the full moon would require the moon to be much higher than the sun (to get illumination on its entire surface). If the full moon was further away, then it would be significantly smaller. The sun must be stable or we would observe massive monthly temperature fluxuations (I'm talking 20-50 degrees C). Therefore, it must be the moon which moves. However, the full moon is not noticably smaller than the lesser moons. This problem was what led Aristotle to first propose the round Earth concept (it was not Columbus, who merely debated the size of the Earth).
The setting sun. The sun on the horizon appears larger than the sun overhead. The Flat Earth proposal is that the sun goes so far away that it appears to set. However, that would involve a shrinking sun, not a growing one. The round Earth explanation for this is that the longer atmosphere (due to the angle) expands the sun's position like a flashlight farther from the focus. Also, more of the yellows and higher spectrum colors are absorbed, causing the red hue. In the flat Earth explanation, one would expect a different effect, where the sun expands and then shrinks below the horizon, not a continuously growing sun which sets.
The conspiracy. The number of people involved are truly enormous, involving every sailor, navigator, and pilot south of the equator for the past three hundred years at least. It is impossible to hide the fact that a trip from South Africa to Australia takes over half again as long as a trip from Vietnam to Algeria (comparing the radii from the North Pole). In fact, the accepted round earth theory says that the Algeria-Vietnam trip will take longer due to being at the equator. Thus, this conspiracy will also have to include every scheduling manager on the planet, many of whom have a vested interest in NOT following it. If it takes X amount of time to ship something from South Africa to Argentina, then it should take 1/2 X to ship something from New York from London. That means, to keep the round-earth conspiracy alive, they must deliberately and knowingly moving across the Atlantic at half speed. Slowing down service is not condusive to profit, so anyone who broke the unwritten rule would immediately snap up huge shares of business in the busiest shipping markets (US to Europe and US to China) on the planet, quickly becoming too public for the government to shut down. Therefore, the conspiracy of people who know or are consciously ignoring the truth must number in the billions
In short, these are the reasons why the Flat Earth Model Fails. Explanations?