We really need to establish what IS flat - does 1 degree of curvature count as being flat? What about an area that has an uphill bit and a downhill bit but the sum of the two would be flat? Are they saying they dont believe in mountains and valleys?
"The Earth is, more or less, a disc," he states. "Obviously it isn't perfectly flat thanks to geological phenomena like hills and valleys. It is around 24,900 miles in diameter."
Hopefully flat or at least concave ovoid. Otherwise it would tumble off. However all is not lost, if the earth was round it would roll over lots and lots of unipeds, bipeds, tripeds, quadrupeds etc. Now if it is flat we all just hear a little rumble and get a little jolt. Incidentally Purple, you're not giving much away as regards the shape of your own little world.