I've never had the courage to dive into that stuff myself, but I've always wondered how they dealt with the stars. it doesn't seem like they could accept the generally accepted notion that they're objects at effectively infinite distance from the Earth, because then how could you account for different stars appearing in the sky depending upon latitude?
I suspect that flat-Earth models sort of fudge the question of what they think is up in the sky, because the sky simply isn't important to them except as a sort of backdrop. flat-Earthism seems to overlap heavily with worshippers of the "literal" Bible, so maybe they figure the sky is little more than an irrelevant light-show that God's seen fit to run in the background of our lives.
~Chara
