So galaxies are falling off the edge of the universe never to be seen again?
The way you've worded this, you're incorrect. There are people today who believe in a flat Earth, crazily enough.
Of course, the idea that most of society (namely educated people) believed in a flat Earth is a myth. From your link:
"The myth of the flat Earth, or the flat earth error, is a modern historical misconception that European scholars and educated people during the Middle Ages believed the Earth to be flat."
What the typical serf working in the fields thought about the shape of the Earth is probably unknown.