On Minimum Wage
As for the first issue--which isn't even his point--I think he shows complete disregard for the economic analysis underlying not having a minimum wage. Contrary to what he thinks, higher minimum wages (special situations involving monopsonies and labour shortages aside) will reduce employment. It's not just the case that companies may not be able to pay their workers, it's often the case that they won't find it be cost effective to pay their workers. Minimum wages have the same problems as unions, in that they provide greater benefits to those on the inside, while simultaneously increasing the number of people on the outside. Of course, that doesn't mean that they're necessarily bad. But the economic problems, including the ways that minimum wages can make the working poor worse off in some circumstances, shouldn't be ignored.
Personally, I believe that there are rights issues involved in these questions, as I believe that a society shouldn't let its most disadvantaged suffer terribly as everyone else gets rich. I believe passionately in equality of opportunity, and I also believe that everyone ought to have a very basic standard. But I believe it's society's responsibility as a whole, rather than the responsibility of certain employers, to make sure that people reach this standard. As a result, I think that a better way than simply forcing minimum wage laws on firms to address such "rights" issues (I think the underlying right is much more complex and may not simply be an unqualified right to a minimum standard of living, but I'll assume now that rights language is appropriate for the sake of argument) is for a better welfare system which guarantees everyone a minimum standard of living and comes out of general tax revenues. A stronger welfare system reaches everyone and distributes the burden on society, not on particular businesses. Under certain conditions, welfare coming from general taxation may also be less distortionary than minimum wage laws, as the increase in taxation required to increase welfare would be much more diffuse and minor than is the burden imposed by minimum wage laws, which are specifically concentrated on specific actors. Thus, I think welfare is probably a more economically efficient, comprehensive, and socially justifiable means of providing help to the working poor than is a minimum wage law.
Now, moving on to the actual argument which Stackhouse was trying to make, I wholeheartedly agree that given that minimum wage exists, it ought to be indexed to inflation. If minimum wage is meant to provide workers with a minimum standard, then it must account for inflation. Indexing minimum wage to inflation reduces workers' risk exposure to the possibility of significant inflation, allows for stability in both real costs for firms and wage rates for workers, and provides predictability for firms, who can accurately predict costs instead of being forced to guess when legislatures will act to change the minimum wage.
Indeed, other legislation recognizes the benefits of indexing. The Residential Tenancies Act 2006, for example, indexes rent increases to inflation. There's no reason why the same couldn't be done with respect to the minimum wage.