Here's a good Cafe Hayek post on the subject of arguments for and against (not about minimum wages directly, there's one level of meta for safety.)
Specifically, they link to this list, summarising the (vast) number of economic studies revealing negative consequences of minimum wage laws, including some non-obvious ones, like
"The minimum wage causes employers to cut back on training."
Hashimoto (1981, 1982), Leighton and Mincer (1981), Ragan (1981).
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?