How did the church authority begin to erode in the mid-11th century?

After the collapse of the Roman Empire in the Latin west, rather than there being a single powerful central authority, there were many different small kingdoms, often vying for power. The Church was the only stable institution spanning the geographical area that had been the Latin West. The Church had a strong institutional structure, a tradition of literacy, and clear lines of authority. It was also extremely wealthy.
As more powerful and stable kingdoms arose, power was increasingly centralized in kings rather than shared among groups of nobles. Kings and kingdoms began to increase in power relative to the Church. Most importantly, kings in England and France began to challenge the right of Popes, located in Italy, to make decisions about appointing French or English bishops and abbots. This led to controversies over investiture, with Pope Gregory VII asserting his right to choose church officials and Henry IV and William the Conqueror, among others, asserting their own opposing rights. This marked the beginning of a series of conflicts between the papacy and various monarchs that culminated later on in the Reformation.
Another weakening of Church authority had to do with popular movements including the Albigensians, Cathars, and other similar movements which often saw the Church as itself corrupted by luxury, and they argued for salvation being available outside the Church as an institution. They weakened the moral and spiritual authority of the Church by offering both theological critique and alternative forms of faith.
http://www.vlib.us/medieval/lectures/heresies.html