I think one thing is this: minimum wage jobs might discourage people from hiring people to do jobs that are potentially high risk and have a chance of producing no positive results (but these same jobs might be funner since they're more creative - or they might use untested labor).
Lots of people are now willing to work for "free" - it's called crowdsourcing (as documented in many books). It might be an extra incentive for them if they have a limited monthly income less than the minimum wage.
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?