What was Mao Zedong's greatest success and his greatest failure?
This is, of course, a question that can only be answered subjectively. There is no way to objectively answer such a question. My own view is that Mao’s greatest success was building a country that was able to remain relatively stable even after his death. His greatest failure was that he did not make that country just and/or prosperous.
Before the communists defeated their enemies in 1949, China had not been united or stable for quite some time. The Qing Dynasty had become very weak in the late 1800s. Numerous warlords started to be the de facto powers in their areas even before the Qing officially fell in 1912. After it fell, China had titular governments, but none of them was truly able to unite the country. Mao was able to defeat his enemies, create the People’s Republic of China, and keep it relatively united and stable until his death. When he died, it did not fall apart. This is a major accomplishment.
However, Mao did not create a just and prosperous society. It may be wrong to expect him to make the country prosperous immediately, but he could have made it much more just. His “Great Leap Forward” and his “Cultural Revolution” were extremely unjust and, particularly in the case of the Cultural Revolution, brutal. Mao’s greatest failure was his inability to create a country in which things like that could not happen.