Mixed economies can enable some government regulation in areas where there is market failure. This can include:
Regulation on the abuse of monopoly power, e.g. prevent mergers, prevent excessively high prices.
Taxation and regulation of goods with negative externalities, e.g. pollution,
Subsidy or state support for goods and services which tend to be under consumed in a free market. This can include public goods, like police and national defense, and merit goods like education and health care.