Galileo questioned the Roman Catholic's dogmatic view of a flat Earth, consequently, leading to the discovery that the Earth is round.
This is patently false. That the world was spheroid was known for centuries before Galileo, and in fact the belief predates the Catholic Church, which never subscribed to the theory of a flat Earth. Galileo subscribed to Copernicus's heliocentric theory at a time when most people still held to the geocentric one, however. Galileo believed he could prove heliocentrism through the study of the Earth's tides. The Pope at the time would have let him get away with it, too, as long as he had included a caveat that it was only a theory, which, at the time, would have been a perfectly accurate statement. In fact, the only real reason to prefer the heliocentric view at that time was that the maths needed to describe the model were somewhat simpler than the ones required for the geocentric one, whereas anyone looking at the sky would have sworn that the geocentric view of the Earth was true based on direct observation (the relativistic effects of motion were not so well known back then). However, in his defense of the theory, which took the form of a dialogue, Galileo portrayed the person who defended the Pope's personal views as a bumbling fool. The Pope was not amused, and ordered Galileo dragged before the Inquisition.
Beyond that, you might want to reference more specific examples in your second body paragraph. Also, overall, you need to include a more in-depth exploration of what exactly the relationship is between technological advancement and authority. The development of the atomic bomb, for instance, was funded by various governments, as was the development of most early spaceflight technology.