This is such a large question that goes over so many bodies of knowledge that I really could be here for days - after all, if we call the Scientific Revolution a revolution, it's because a whole host of previous understandings were overturned. So please forgive this answer being something of a greatest hits version of an answer.

What we'd now call scientific knowledge in Western Europe in the late medieval era was based heavily on classical Greek philosophy. If you learned astronomy, it was based on Ptolemy's conception of the Earth's relationship to other celestial objects; if you learned physics, it was based on Aristotle's conception of causes and substances; if you learned physiology, it was based on Galen's conceptions of the structures of the human body. And of course, each of these classical Greek bodies of knowledge were hugely challenged in the Renaissance.

In terms of Galen, the publishing of Andreas Vesalius's The Fabric Of The Body in 1543 provided one of the first big challenges to Galen's physiology - Vesalius was an enthusiastic dissector of human cadavers and identified scores of errors in Galen's work. Because of the taboos of the time, Galen had dissected animals and generalised to human anatomy, and Vesalius demonstrated that these generalisations were often incorrect; e.g., Galen thought we had a rete mirabile, an anatomical structure present in many other vertebrates (dolphins use it as a swim bladder, giraffes use it to pump oxygen up their necks). But humans don't have this anatomical structure, as Vesalius identified (and because of the advent of the printing press, he could provide pictures and diagrams in a way Galen couldn't, which helped people believe him over the ancient authority of Galen). Similarly, Leonhart Fuchs' 1542 On The History Of Plants demonstrated several inaccuracies in Galen's botany, and Fuchs referred to Galen as 'the most insipid authority' in the introduction to the bood. Going back to physiology, Galen had believed that blood evaporated upon reaching the extremities; William Harvey's 1628 book demonstrated that blood circulated through the body, pumped by the heart.

In terms of Ptolemy, instruments like quadrants and telescopes in the Renaissance/Scientific Revolution could measure the movement of celestial bodies much more accurately than anything Ptolemy had. Between the work of Copernicus, Brahe, Kepler, and others, it became clear that the notion that the Earth revolved around the sun in an elliptical orbit explained the data rather more accurately and simply than the Ptolemaic notion that the Earth was the centre of the universe. The standard late Medieval/Renaissance textbook on Ptolemy's astronomy was Sacrobosco's Sphere from ~1220; the last edition of this was published in 1633, which Wootton argues is the point where Ptolemaic astronomy finally becomes dead in the water.

In terms of Aristotle's physics, the Aristotelian notion that the world was made of two spheres - a sphere of earth floating in a sphere of water - didn't really survive Columbus and Vespucci's trips to America. It was obvious post-Columbus/Vespucci that the existence of the Americas simply didn't fit with the idea that the earth was a sphere floating in a sphere of water. Aristotelian physics were shown to be pretty problematic by the early 17th century work of Galileo; Galileo famously showed that a) objects accelerated as they fell and b) that if you accounted for wind resistance, heavier and lighter objects fell at the same rate. Similarly, Aristotle believed that vacuums were inherently impossible, but the vacuum pumps of people like Boyle and Torricelli in the 1640s-1660s appeared to show that vacuums were possible after all (though it took rather longer to figure out whether the ability to see the vacuum inside a vacuum pump meant that it wasn't entirely a vacuum, because something had to be conveying light through the vacuum). And that's without getting into Descartes' mechanical universe and Newton's laws, which saw the universe in profoundly different ways to Aristotle.

Source: David Wootton's 2015 The Invention Of Science: A New History Of The Scientific Revolution.