Adam Smith's faith in the free market is one area that would provoke intense disagreement from Karl Marx.
A major component of Smith's analysis is his belief that the free market that can function without external control. Smith believes that the marketplace is where human happiness can be maximized. The free market is where human talents are recognized. It is where goods can be exchanged for compensation and services. Smith believes in the "laissez faire" approach to the marketplace so much that he rejects the idea of controlling it. For Smith, control is needed for something bad, and if the marketplace is where the greatest in human endeavor is realized, then controlling it would actually be a bad thing. Even if there are problems in the marketplace, Smith argues that the "invisible hand" of rationality and reasonability will solve everything, thereby rejecting the need for external control.
Marx would take issue with this emphasis on the marketplace needing to be free from external control. In Marx's mind, the freedom afforded to the marketplace has enabled economic exploitation. It is the freedom to have a small number of very rich people take advantage of the working class majority. Marx would challenge Smith's belief that the free market is where happiness can be seen. Workers in the free market configuration are not very happy when they are working long hours for little in way of compensation. Their happiness is not realized in Smith's "laissez faire." Marx would reject Smith's idea that the marketplace does not need external control. In a setting where economic exploitation is so rampant, Marx would argue that external control is needed in order to facilitate a new and more equitable economic system.