I do not know if any/all of these have been mentioned in the past, but here are a few items to consider:
First, why is the shadow of the Earth on the moon round during a lunar eclipse?
Second, if the earth is flat with the north pole in the center and Antarctica around the edges, why are Mercator-projection naval navigation maps not horribly inaccurate? If your model is correct, we should be using polar coordinates to navigate, not cartesian coordinates. I.e., England is not truely due east of Canada, it is counterclockwise.
Third, if Antarctica is a ring of ice around the edges, how have people transversed that continent? Were they all in on some conspiracy?
Fourth, why do experiments like that of Eratosthenes, where the shadow length of two poles a certain distance apart north-south is measured to differ, show different shadow lengths if the surface of the globe is flat? This experiment is easily reproducible with some advance planning; simply have two parties in two spots far enough away.
I am legitimately interested in hearing some responses to these questions. I apologize if these questions are answered by some base section of Flat Earth theory; I cannot claim to be anything but ignorant on the specifics. But I would love to be enlightened! So, any response is encouraged!