How did the Mandate of Heaven cause problems for the leadership and power in China?

The Mandate of Heaven meant that the emperor was ruling with the blessing of the gods. This belief gave the emperor a degree of legitimacy. However, if things were going badly, such as in the case of a drought, famine, earthquake, or popular revolt, the people could turn against the emperor. In these cases, the people might believe that the emperor had lost the Mandate of Heaven and that the gods were no longer in support of him. The emperor's rivals could argue that they possessed the Mandate of Heaven and were the rightful rulers.
In ancient China, rivals to the throne often claimed that the emperor currently in power had lost the Mandate of Heaven and that they had this Mandate. For example, the Zhou dynasty claimed that the Shang dynasty had lost the Mandate of Heaven and overthrew the Shang around 1046 BCE.