Hello, I am Mr. Anon, and I'm kind of new here. I am familiar with many experienced physicist, and as a result here are some scientific observations I have made about the Flat Earth notion.
Gravity
First off, this is the biggest thorn in the FET in existance. Gravity has been proven; I have seen experiments that display very small forces between two masses. This poses a significant problem for the Flat Earth. Even a very thin disc the size of the Earth would have a mass large enough to fold itself into a sphere. The Flat Earth version of gravity, the proposed Universal Accelerator, simply does not work. Even at the creationist view that many Flat Earthers embody, where the Earth is only 6000 years old, the disc, accelerating constantly at 9.8m/s/s, would have long ago exceeded the speed of light. While this can be explained to an extent with relativistic effects, the result is that the rest of the universe would rapidly age compared to us, and as we approach the speed of light, the acceleration we feel would decrease. In addition, the energy required to maintain such an accelerator would be tremendous (I don't even want to calculate it, though I could, as I'd have to add the masses of the Earth, planets, and the Sun and Moons). In addition, the UA does not account for the observed slight decreases in acceleration that have occurred at higher altitudes.
Ice Wall/Antarctica
The Ice Wall also poses some challenges for the FET. There have been recorded journeys that have been made across the Antarctic continent, as well as some plane travels. In addition, the inside circumferance of such an Ice Wall would be far greater than the measured circumferance of Antartica, and also would contradict nautical journeys, where (going clockwise according to the North Pole) sailoirs would end up constantly turning West instead of East. I am aware of a second FET map, where Antarctica is still and island-continent, but this map severely distorts the Pacific Ocean, and also does not create any means of keeping water from spilling over the edge of the Earth.