One of the weaknesses, as noted, was the corruption of the Catholic Church as noted by Chaucer in The Canterbury Tales. One of the previous posts spoke of the sale of indulgences (with a great quote), and the Pardoner in Chaucer's story is one of the corrupt servants of the church who sold stolen indulgences, as well as fake artifacts—a piece of cloth said to be from the Virgin Mary's veil; another the sail of the ship when Peter walked on water with Christ. Though Chaucer does not directly censure the Pardoner, we can read between the lines. And the story the Pardoner shares with the group of pilgrims speaks of the death of three men because of their greed.
The Protestant Reformation was obviously an unwelcomed development. The Church also had to face the plague, which swept Europe twice—the Church tried to explain it away as punishment for sin. They were no more able to explain in than anyone else, but populations died, giving decreased, the Church's servants and workers died...it was a difficult time for everyone.
Division within the Church caused serious problems, while things were in chaos around them.
However, the Church's failure to move away from tradition could have been both a blessing and a curse. Those looking for change did not find it in the Roman church; however, those who felt comfortable and safe, especially facing plague and war, would have taken comfort from the unchanging Church, especially when so much around them was changing—and death was everywhere.