Market failures are everywhere! Read a newspaper or web site and you’ll quickly find pundits saying that the market has failed to solve such and such problem. Most of the claims have to do with the market’s supposedly inability to provide the "correct" quality and quantity of a good or service. Let’s correct this misunderstanding.
The market is the sum of all of the individuals who are participating in exchange. When there is (free) exchange, A gives B something that A values less than what B is willing to give A in return. In this double inequality, both parties benefit.
There’s no need to call the market "perfect" or "imperfect." This is not because humans are perfect but because people engaging in voluntary transactions expect to mutually benefit. Thus, their expectation of gain is true every time, otherwise they would not trade. In this narrow sense, we can correctly say that the market is efficient. Buyer and seller are better off and thus are wealthier than they were before ("wealth" is used in the economics sense and not the financial or monetary sense — people become wealthier as they achieve their goals and these need not be financial).
A "perfect" market would imply that every participant is free of error. Every transaction would always be correct and no one would have regrets or would have preferred an alternate course of action. If that were true, however, then this would mean that preferences do not change; that buyers are never swayed to improve their lives by seeking different products or services (or refraining to purchase and save instead); and that sellers and entrepreneurs never change their product lines or seek to improve quality of products. In fact, the exact opposite is what we would expect from imperfect human beings who exchange in order to improve their state of affairs. The discovery of error after exchange is crucial for the advancement of society.
Notice that the market failure crowd tends to criticize specific sectors of the industry, mostly notably health care, education, transportation and sometimes agriculture. Yet these just happen to be some of the most intervened sectors of the economy by government. There is no free exchange and no real chance to opt for a different product. The government "customer" is forced to pay for it all. We see no crisis in the pencil industry, or the computer industry, or in the restaurant industry. Why? Because people in certain sectors of the economy are relatively free to choose, and entrepreneurs are free to search for opportunities to satisfy the needs of others.
Where the critics of the market ultimately fail is when they compare the market to a standard that does not exist. There are no flights to Jupiter or Mars or the Moon even though I want such a thing. Where is the failure? If we understand that the market exists only whenever there is exchange, there is no such failure to be found. Entrepreneurs and consumers have decided that resources are better invested elsewhere and these resources will be able to better satisfy consumer needs. The best way to efficiently make humanity better is to completely allow free markets in everything.