What about people who've circumnavigated the Earth? Are they all lying? Plus, if the Earth is flat, there should be pairs of places you can't get to without traveling in what would seem like the "wrong" direction, like you might have to fly over New York and Europe to get to the Philippines from Hawaii. Where are those "you can't get there from here" pairs of locations?
Where do the polar ice caps come from if the Earth is flat? Why does the sun come only 38 degrees above the horizon on June 21 in Anchorage, but almost overhead in Miami? Come to think of it, if you place a call to Miami when it's noon in Anchorage, why do they insist it's 3pm?
Erps, meant to say “4pm” in Miami at noon in Anchorage.
Also, depending on where the edge is, it should play havoc with expected propagation of seismic waves and tsunamis. There would have to be a discontinuity somewhere that would lead to results unexpected by “round earthers”.