This is 100% inspired by Tom Bishop.
While I believe the earth to be round, I have noticed that RE'ers are simply wrong most of the time. False evidence, hasty assumptions, appealing to the popular opinion, and generally just being stupid. Why are so many of us RE'ers content to be ignorant of our own errors?
The point: what experiments out there are conclusive in one way or another?
Remember, many experiments have absolute conclusions that we assume imply a round earth, yet can be explained by the flat earth model as well. Avoid these. Isolate your variables, what experiments are really out there?
The only ones I can find 1) have never been done so they are moot and 2) rely on a dichotomy of either RE or FE, other options or modified models are not included, which isn't very scientific. Both models will be modified by time, if a test doesn't hold in the future, it shouldn't hold in the now.