Here's a new one for you. I live in Ohio, and we have an interesting phenomenon in the winter around here. The sun is always low in the sky, and while that is, by itself explicable in both theories, I have an interesting point that is only possible on a round earth. The path we see in winter is the sun rising low in the southeast, then drawing closer to overhead (it never gets all that close, but the closest it ever is to overhead is distinctly noon, as ANYONE can observe. In the FE theory, the suns orbit which, in winter, would certainly be lower to the horizon, should be much more equidistant at all times than on a RE. I wish I could render an effective image to demonstrate this, but 1, it'd be called part of the conspiracy, and 2, I suck at drawing, so it really wouldn't clear things up so nicely. JUST CONSIDER THE GEOMETRY.
On a separate point: if the Sun's surface is concave, then the light coming from it has a focal point, like a mirror. I have no ABSOLUTE proof this doesn't exist, but I'd like to point out that a focal point between the Sun and the Earth would be readily visible, as everything passing through it would be vaporized (imagine all the energy the sun exerts all over earth at one instant, but concentrated onto a single point). if the focal point is behind earth, then the sun would have to be ENORMOUS (much larger than the earth itself, which isn't consistent with FE theory as is posted in the FAQ), and it should be noted that this would result in decreased energy as altitude increases. This is verifiably not the case.