If there is one thing that was most questioned during this time, I would say it was "authority." That covers a great deal of the sort of questioning that was going on at that time.
Perhaps the best example of this was Galileo, who questioned both the authority of past scientists and the authority of the Church. Galileo did not simply believe in the Ptolemaic view of the cosmos just because it was the accepted authority. Instead, he questioned it and conducted his own observations to see if it was accurate. Similarly, he did not accept the Church's authority when it told him he was wrong.
During the Renaissance, there was a great deal of questioning of authority as people started to want to think for themselves and draw their own conclusions about the natural world and even about religion.
In my opinion, I feel the most questioned was of religion and its place in the lives of those within the goverment,and those living during the Renaissance. Many were leaning towards secular views becuase of many reasons. The renaissance focused on theology, science, reformation, and the plain factor of corupt religious leaders and churches.
Not only did science divide religion but religion divided religion. With the uncertanties of the Catholic Church many broke off into the spark of the Protestant Reformation.
With these uncertanties of the church and religion this created a huge debate as to wether religion was ultimatly the right way to go.
Great examples of religion being questioned or debated would be: The theologian Martin Luther, Concilariasm (sought to limit the pope's power), Pope Alexander VI, The Scientifc Revelution.