I don't think he did anything more for humanity than most other good-hearted people, to be honest. Not to dismiss the man, I'm hardly aware of his life story, but I also feel that I don't need to be.

If you are hardly aware of his life story how can you make an informed decision on what he did or did not do for humanity?

Why does the world seem to be completely insane?

Yes, it always appears that you are in a minority of sane people (or perhaps you are the ONLY sane person) in a sea of completely confused crackpots. The reason that so many other people seem completely confused and wrongheaded is that they use different symbols and metaphors to view the world. It is impossible to discuss important issues such as politics, families, violence, justice, etc. without resorting to symbolism. Anything that does not directly refer to something that can be physically sensed, such as justice or one's concept of God must be referred to by metaphor and symbol. If you and another use different symbols, you will be unable to communicate effectively. Some of the main metaphors in use today are:

Conventional religion
Science
Power, that is, dominance and submission
Artistic and aesthetic worth
Traditional political categories
Material wealth and security
Romanticism and relationships
Honor, valor, and courage
Bigotry, racism, and exclusivity
Depth psychology (Freud, Jung, etc.)
Humanism and "new age" psychology
Traditional philosophy

Chances are that your views and beliefs about the world center around one or several of these metaphors. For example, if you see the world in terms of moral worth and submission to a higher law, you are conventionally religious. If you see the world in terms of cause and effect and experimenting to find the right solutions, you are oriented toward science.

People who share one or more basic metaphors will find that they can communicate effectively with one another and work together constructively. People who do not share any metaphors will usually be unable to regard one another with anything beyond fear, hostility, and contempt. Because of this lack of communication between groups, most discussions of important issues in the public arena quickly degenerate into grandstanding and name calling, because in the absence of real understanding between the disagreeing parties, only mob psychology is left to sway public opinion.

In all of this you may be left frustrated and unable to act, because you have not yet realized that:

The World Doesn't Want to be Saved.

The world is a teeming mishmash of cultures with a bewildering array of values and ideologies engaged in their own version of the good life. People are generally not interested in changing the metaphors through which they view the world, so real understanding between groups with conflicting viewpoints is not achievable in the short term. The good news is, that's OK, because the world isn't supposed to be saved on a global scale. It must be saved at the level of the individual. And despite the fact that the level of the individual appears to be statistically insignificant, it is in fact the most significant, because it is only at the level of the individual that a creative synthesis of conflicting metaphors can occur. Once a connection is made at the individual level, the process of spreading successful new metaphors throughout society is essential automatic if the society is ready for them. If the society is not ready, the new metaphors will not be accepted under any circumstances. So don't beat you head on a rock. Solve your own interpersonal communication problems. If the world is ready to benefit from your solutions, you will not be able to stop it from using them.

I can't.

Mandela was just at the right place at the right time.

Looking at specific deeds of an individual is to miss the point entirely about how much good they've actually done for the world.