The 2014 OECD employment outlook argued for modest minimum wage increases while at the same time setting out all the steps necessary to manage the unintended consequences of minimum wage regulation:
Mandatory minimum wages, which now exist – or are being implemented – in 26 OECD countries and a number of emerging economies, can help underpin the wages of low-paid workers.
Evidence suggests that, when set at an appropriate level, minimum wages tend to have only a small adverse effect on employment.
Sensible minimum-wage design includes: taking account of differences by region according to the average income level, as well as by age in experience and productivity; ensuring that the level and adjustments of the minimum wage involve independent commissions; and reducing social security contributions to lower non-wage labour costs at the minimum wage (Emphasis mine).
George Stigler made very similar criticisms of the impracticality of a single minimum wage in 1946:
If an employer has a significant degree of control over the wage rate he pays for a given quality of labour, a skilfully-set minimum wage may increase his employment and wage rate and, because the wage is brought closer to the value of the marginal product, at the same time increase aggregate output…
This arithmetic is quite valid but it is not very relevant to the question of a national minimum wage. The minimum wage which achieves these desirable ends has several requisites:
1. It must be chosen correctly… the optimum minimum wage can be set only if the demand and supply schedules are known over a considerable range…
2. The optimum wage varies with occupation (and, within an occupation, with the quality of worker).
3. The optimum wage varies among firms (and plants).
4. The optimum wage varies, often rapidly, through time.
A uniform national minimum wage, infrequently changed, is wholly unsuited to these diversities of conditions
Modest minimum wage increases must varying in their modesty by individual worker quality, occupation, region, firm and plant and the extent to which this modesty can be excessively immodest can change rapidly through time. Little wonder that the OECD refers to minimum wage regulation as a careful balancing act.
In sum, to avoid throwing a good number of low paid, low skilled workers onto the scrapheap of society for the sake of their more employable co-workers, the minimum wage pretty much be set separately for each individual worker. The labour market does that now.
Utopia, you are standing in it! 
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