1) During a lunar eclipse, when the Earth's shadow is cast upon the moon, in every case - it's round, alas you said it could just be a flat circle.
2) As Jared said, ships 'falling off' the horizon is a big tell that the Earth is round, but you've discredited this too, by assuming the atmosphere can deflect the light causing the ships to 'disappear' at far distances. Let's keep going..
3) Star constellations vary depending on where you are, if the Earth were flat, you should be able to see the same star constellations no matter where you were, however this isn't true as they are different for the northern and southern hemispheres. However, if you'd never travelled to another country you wouldn't know this to be true either, so let's move on.
4) Stand at the bottom of a flat plane, look out with your binoculars as far as you can see. Climb a tall something - a tree/ mountain, whatever, you will see more than you could see before, due to the curvature of the Earth. Hard to find a flat plateau with just one tree though..
5) Get on a plane, look out the window, Earth looks round right? It is. The plane can keep going in a 'straight' line and never get further from the Earth, or fall off it, or fly past it. The plane's travelling round the Earth and circling it's roundness.
6) Take a look through your telescope ( I know, you'll disprove this one too by saying not everyone has a telescope) and you'll see all the other planets appear round too, no matter when you look at them, is they were flat, sometimes you couldn't see some of them as they would be side on.
7) Timezones: i.e In new york, it could be night when in the UK, it's daytime. Prove this by calling someone up, skyping them, you got proof! A flat world would be all day, then night.