If you think about it, the most predictable harms should come from the same mechanisms as the benefits. And the mechanism? Complicated economics. Or at least that's the mechanism I'd like to emphasize, since it's harder to quantify the other ones.
And what do I mean when I say complicated economics? I mean http://en.wikipedia.org/wiki/Monopsony#Minimum_wage . Look at the diagram to the right. It took me about an hour of actual work to understand what that diagram means to the minimum wage, so no rush.
The concept of minimum wage is one I'm rather attached to. I have dozens of arguments for why it helps people, improves the world, etc. etc. I suspect this view is shared by most of this community, although I haven't seen any discussion of it.
I don't have much understanding of the harms that minimum wages cause; and at what level of minimum wage those harms become relevant (ie. a minimum wage that would not be a living wage even working 24 hours a day is unlikely to have any of the same problems that a minimum wage sufficient to buy an aircraft carrier an hour would have)
So what are the harms that such laws cause?