Economics is great for telling us about these hidden costs, and I agree the minimum wage example is a good example where the costs outweigh the benefits. But it's not a clear-cut libertarian case of "all things that cause economic inefficiencies are bad policies". All economics can tell us is approximately how much inefficiency, for instance, would be caused by subsidized food stamps. It's up to everyone to learn what that cost-benefit is and decide whether we can afford to subsidize some folks' food purchases. (Food stamps, and voucher schemes in general, seem to work well in my opinion.)
Or conversely, if we come down and say we want to reduce sulphur dioxide emissions, we might say, "Oh, let's inspect and license all the smokestacks in the US and write each of them permits every year." Economists will shake their heads and say that's an inefficient allocation method, and then they will invent cap-and-trade, where we sell them permits and let them trade the same fixed number of permits, so that SO2 emissions stay under a determined scarcity, but that scarcity is market-allocated. We've been doing that with SO2 for years and it's one of the great recent triumphs of economics.
But you've ignored decades of economists explaining how to do social programs in an efficient way. For example, Milton Friedman's Negative Income Tax would take the place minimum wages and food stamps with none of the administrative overhead or perverse incentives (i.e. the "welfare trap," where earning an extra dollar per day results in losing more than a dollar per day in benefits, thus discouraging career advancement).
And wrt sulpur dioxide, economists since Pigou have been arguing not for cap-and-trade, but for pollution taxes to right externalities. And if you go beyond Pigou, you don't find cap-and-trade, but Coase, who argues that if you structure the system properly, you don't even need intervention to right externalities, the actors will find an efficient arrangement on their own. Even beside this, Libertarians have no principled opposition to righting negative externalities: it's one of the few proper roles of government.
In the end, cap-and-trade is preferred not because it's the most effective, but because it's the most politically expedient. Pollution/Source fuels taxes are cheaper to administer, have better incentives for bureacrats to be faithful, and achieve the same ends. They're better and economists will tell you so. The only reason cap-and-trade is the solution-du-jour is because it doesn't include the word "tax" in it. This is why conservatives are identifying it (correctly) as "Tax-and-trade."
You're not arguing against libertarians, you're arguing against the decades of economists you (I'm sorry to say) don't seem to know.
Or conversely, if we come down and say we want to reduce sulphur dioxide emissions, we might say, "Oh, let's inspect and license all the smokestacks in the US and write each of them permits every year." Economists will shake their heads and say that's an inefficient allocation method, and then they will invent cap-and-trade, where we sell them permits and let them trade the same fixed number of permits, so that SO2 emissions stay under a determined scarcity, but that scarcity is market-allocated. We've been doing that with SO2 for years and it's one of the great recent triumphs of economics.