Corruption was the main problem in the Medieval Roman Catholic Church. Even though priests, monks and nuns took vows of chastity, obedience, and poverty, they were sometimes not kept. Priests (and even some popes) had children, for example.
Corruption also extended to government power. One of the reason the United States of America advocates the separation of Church & State [i.e. the government] is that the Catholic Church sometimes worked with kings to help them get their way. The Church sometimes also had the power of excommunication and final pronouncement on many issues with huge ramifications, such as the divorce petition of Henry VIII vs. Catherine; it was one of the spurs for Henry VIII to break away from the Church and create his own, the Church of England.
As stated above, Church authorities (cardinals, bishops, archbishops and the pope) often meddled in secular politics to get a result most favorable for the Church.
The Catholic Church was also very wealthy. The land and wealth of people who died without heirs sometimes went to the Church. When rich people did bad things, they were sometimes asked to donate land to the Church and build a cathedral, monastery or abbey on it. People left land and material goods to the Church to have [what they thought was] a better chance of getting into Heaven.
The Church also made a great deal of money selling things, as well as scam artists in the name of the Church. Saints' bones, hair, clothing, etc. was sold (and was rarely real) to help bless the person who possessed it. Divine intercession could be bought; if you or a loved one had lived a sinful life, you could buy "leftover good" (left over from Jesus and the different saints when they were alive on Earth) to guarantee entrance for your family into Heaven.
Medieval life in Europe was centered around the Church. Peasants and serfs were promised an amazing afterlife if they respected their betters and lived a good life on Earth. This helped alleviate the discontent of extreme poverty and no control over their own lives.
People like Martin Luther (a Catholic monk who later founded Lutheranism) were offended by the corruption of the Catholic Church and created their own religions based on Catholicism, but with less corruption.