There is the International Space Station, which floats in space above the earth. I don't know how the flat earth idea accounts for that or any other satellite floating in orbit. Obviously there are satellites floating over the earth because we have GPS, satellite telephones, satellite internet, and other things. So how do those satellites stay suspended over the earth? Why don't they fall down? They don't have rockets continuously blasting downwards to keep them in the air.
Another thing that I thought of from another thread, distantly related to this, is how a compass works. The globe earth believes that the earth is a giant magnet, and a compass works because the needle is magnetized and drawn to the north and south magnetic poles. According to the flat earth model, Antarctica is not a continent but a wall of ice around the edge of the earth. So, where exactly is the southern magnetic pole? It must be somewhere. Let's say it's just south of Tierra del Fuego, South America. If it were there, then when you went to the Cape of Good Hope, you would be roughly east of the south magnetic pole, so the southern end of your compass needle would point towards South America, not Antarctica. And depending on where you went in the world, the direction the compass needle pointed would be dramatically different.
I have still not heard an explanation for how the sun moves in the flat earth system. Flatties claim the sun moves parallel to the ground, and in a horizontally circular motion. Both those things are independently impossible, and for different reasons. When you throw a ball through the air, it falls to the ground, it does not move parallel to the ground for even one instant of its trajectory. Moreover, an object cannot move in a horizontally circular path through the air because it takes force (centrifugal force, I believe it would be) to make something move in a circle. Unless you're talking about a boomerang, which the sun sure doesn't look like, objects move in a straight line relative to the ground when they are flying, in the sense that, if you were to throw a rock and then draw a line on the ground that precisely followed the path of the rock through the air, the line would be straight. It would not be curved.
There is no example in nature of any object being able to move in the way the flat earth system claims that the sun moves. It effectively claims that the sun (and moon) are exempt from the laws of physics.
Now, the sun in the globe earth system (whether you choose to heliocentric or geocentric model, it makes little difference) simply behaves in a manner that we see numerous other objects moving in space, so that we know for certain that such motion is physically possible. You can look at Jupiter and see its moons rotating around it in a circular motion. The globe earth simply says that that is how the sun moves around the earth, or the earth around the sun, or whatever. That is also the type of movement that we claim the satellites use that orbit the earth, that make possible GPS systems and other stuff. No one needs to posit ad-hoc explanations or invent phenomena that aren't otherwise known to exist to explain any of these things.
EDIT: typo