Those thinking that capitalism most lead to a harmful oligopoly should read this thread. Skip to my last posting if in hurry. Read for example the history of why the Sherman act was created:
https://www.physicsforums.com/showthread.php?t=47769&page=5&pp=15
That there is a oligopoly in many markets is not an argument in itself. That reflects that fact that in those market that is the best structure, for example markets requiring very large investments cannot have many small competitors. Those arguing otherwise must show that oligopoly is more harmful than some regulated alternative, not that it exists in some cases.
There are those who for various reasons have less ability and may not be able to compete. But they would have those difficulties in any system and they must be supported by the others. That is charity, no matter if it is done by the state or individuals. And as I have pointed out in this article before, why cannot charity have competition and efficiency like other sectors of society?
Regarding medicine, it is no different than any other market. The demand is endless, for example it would be good if all people could have an complete body MIR scan and interpretation by the very best radiologist every year. But since that is not possible, the free market is the best way to organize the limited resources available.
Regarding the tennis shoe example, firstly there should be the possibility to sue for things like false advertisement or malpractice, secondly competition is not done by one individual but by many. And people are learning from the mistakes and experiences of others. This can be a market in itself, like magazines doing reviews of computer games, cars or various household devices.
There are of course problems in capitalism that may require limitations. One very interesting theoretical one is "The tragedy of the anticommons". But I think it is actually an argument that there are some property rights laws that are better than others, not an argument against property rights in itself. That problem can be solved by competition between many small states that have somewhat different laws.
http://www.sciencemag.org/cgi/content/full/280/5364/698
Other proposed problems (often imaginary or having good if less than perfect solutions or with no proof that there exists better solutions):
http://en.wikipedia.org/wiki/Market_failure