Devil's Advocate here:

Aurora at both the North and South Poles This could happen with a flat earth Coriolis/Eotvos effects Yeah, couldn't really happen with a flat earth I guess, but these effects are so minuscule they cannot be measured. For instance, the differing directions (clockwise/anticlockwise) of storms depending on which hemisphere they are in is completely inconsistent and proves nothing. Snipers rarely use it (and if they do, how do we know it works?), and planes don't seem to use it. Cars don't use it. I don't know why it is something that people discuss so much. Equal daylight hours from Summer to Winter at the Equator You could do this with the flat earth model. Daylight hour differential grows larger as you travel North or South I'll have to think about this one. Six months daylight/night at both the North and South Poles I think this could be possible if the sun is low. Equator has warm weather year round, Winter gets colder as you travel North or South Will have to think about this one too Different star constellations in Northern hemisphere versus Southern This is difficult to prove with flat earth... I agree with this one Center of rotation around one star at both North and South poles This is difficult to prove with the flat earth model because the south pole is basically the entire circumference of the plane(t) Objects appear to drop below the horizon They don't though. This is an optical illusion. They just fade into the distance. Lines of latitude are longest at the equator, and grow shorter as both the North and South poles are approached The flat earth model could make this work for the North Pole, but the South Pole would be difficult. Magnetic field This could work with a flat earth model. Equal gravity at every point on the surface of a sphere (on a flat disk, gravity is strongest at the rim and weakest at the center) On a flat earth, gravity could be constant depending on what is outside of flat earth. On the globe earth, the force of gravity is (theoretically) offset by the earth's centripetal force - which varies depending on what latitude you are on... so the force of gravity on the round earth is not constant. Global Positioning System This is really not just satellites. Look up WAAS - GPS relies on cell towers to work. Phases of the Moon - Lunar and Solar eclipses The Mayans could predict all this stuff, and they believed in flat earth Phases of other planets (e.g. Venus) Don't know much about this Unlimited line-of-sight radio communication is possible on a flat earth, but not a sphere Can't they bounce radio waves off the atmosphere or something? I'll have to look it up.