1. Most markets are oligopolies dominated by a few companies). For a market to be able to ensure sufficient competition individual companies should be not be able to significantly influence market prices. Economics text books acknowledge this.
2. Many markets are natural monopolies and therefore rely on regulation rather than market forces to set prices and determine what services are provided. Examples include utilities and fixed line telecoms.
3. Regulators are not always able to effectively deal with monopolies and cartels. Reasonably clear examples of this failure include computer software and some media.
4. Markets do not take account of negative externalities: the damage done to others as a side effect. Examples of externalities include pollution. The usual solution is regulation or some attempt at costing. There is no practical way to guarantee that the end result of such regulatory action will result in a optimal outcome.
5. Markets do not take account of positive externalities and the production of public goods. The purported solution is to provide a wide range of incentives such as grants, temporary monopolies (patents and copyrights), and regulatory requirements. Again, there is no way to determine exactly what incentives will give the best result.
6. A specially important aspect of this is that there is no free market mechanism for funding research and development that we know is efficient. Economists can show that a competitive market will lead to the most efficient use of resources in production or in providing services, this can not be done for R & D.
7. A lot of regulation is designed to help producers rather than consumers. This is the opposite of what should happen in a free market. A good example are EU rules allowing only producers in certain regions to sell goods under certain names (e.g. parma ham must come from Italy).
8. Most technological products are too complex for consumers to make proper assessments of products. Good examples include the common misconceptions that a computer with “more gigahertz” is faster, that a camera with more mega-pixels is necessarily higher quality etc.
9. Many markets are regulated in ways that distort the market. For example building a certain amount of low cost housing may be the price a developer pays for permission to build luxury housing. While the result may be socially desirable, it amounts to an unpredictable tax on certain types of activity, which must distort a market.
10. Some pricing structures allow people to choose costs that will be imposed on others. For example, if you phone me on a mobile phone, you pay a price that is partly determined by my choice of phone company (assuming calling party pays). The solution to this is, again, usually regulation of prices. Again, bye to the market setting prices.
11. Governments frequently set or support certain prices for economic or political reasons. The best example is the subsidising of agriculture in almost all countries.

Given how many major industries are subject to one or more of the above (IT, telecoms, media, agriculture, food, retail, electricals retail……), it appears that we do not have a free market economy, we have bits of free market economy is a sea of regulated capitalism. The most worrying aspect is the high and rising degree of central planning.