This means that in an economy with some unavoidable market failure in one sector, there can actually be a decrease in efficiency due to a move toward greater market perfection in another sector. In theory, at least, it may be better to let two market imperfections cancel each other out rather than making an effort to fix either one. Thus, it may be optimal for the government to intervene in a way that is contrary to laissez faire policy. This suggests that economists need to study the details of the situation before jumping to the theory-based conclusion that an improvement in market perfection in one area implies a global improvement in efficiency.
Even though the theory of the second best was developed for the Walrasian general equilibrium system, it also applies in microeconomic (partial equilibrium) cases. For example, consider a mining monopoly that's also a polluter: mining leads to tailings being dumped in the river and deadly dust in the workers’ lungs. Suppose in addition that there is nothing at all that we can do about the pollution. But the government is able to break up the monopoly.
The problem here is that increasing competition in this market is likely to increase production (since competitors have such a hard time restricting production compared to a monopoly). Because pollution is highly associated with production, pollution will most likely increase. This may actually make the world worse off than before.