In order for the concave earth to match up with observations, light has to curve upwards. However, if light curves, it will make objects seem lower than they really are. That means that whatever altitude we observe satellites at, they will be higher than that. According to both theories, the diameter of the earth is 12,756 km (source). Geosynchronous satellites can be observed at an altitude of 35,786 km (source). That puts them far beyond the other side of the earth if it's concave, and it must be even higher if light curves upwards.

For satellites to work, the earth needs to be convex. Satellites aren't equipped with anything by which to glide, slide, or hover over a glass layer, and they would have to expend massive amounts of fuel while traveling across the layer in order to emulate the paths that orbits would take them. Furthermore, satellites travel at many varying altitudes, but the glass layer accounts for only one of those.

In order for the readings we get from earthquakes to make sense, the earth has to be a globe with a metal core. Seismologists can compare readings from all over the world to study the refraction of vibrations from distant earthquakes. Not only does this show the internal structure of the earth, but it also allows us to hear where the bits of subducted crust are.

This brings me to the tectonic plates. In order for the plates to move (and they do move, however slowly) the mantle must carry them by convection. That is, the mantle gets hot near the core, rises up, cools, moves to the side, and sinks down. This is the same thing that happens in a pot of boiling water or a convection oven.

Furthermore, the rotation of the core is what gives us our magnetic field. The magnetic poles of the earth are not constant, which proves that whatever is creating the field is not rigid with the earth.

The moon is a large spherical rocky body that is responsible for tides and orbits by the same mechanism that satellites do. We can see that the moon is spherical by observing that it librates and that shadows travel across its surface as they do with other spheres. This is further confirmed by the shadows cast in the craters. The reason that the moon does not appear to have parallax is that it is more than a quarter million miles away. We know that the moon is reflecting the sun's light because the lit side is always facing the sun. If the moon were not a massive body, it could not create the tides.