What we do not know about the minimum wage

We were discussing the minimum wage last week in my MBA 505 Global Economics for Managers class.  Bloomberg columnist Megan McArdle did a nice job in a recent column summarizing the economics research literature.  Did she read literally 100s of papers?  I kind of doubt it, but she reaches three main conclusions:
1) Most people have their own opinions about whether the minimum wage is a good or not so good idea and they naturally seek out and site research that supports their own opinions.  Psychologists call this confirmation bias.  As is always the case in economics, you do not have to search very hard to find a study that matches your views.  Some find big job losses, others find small job losses and one very famous study found no job losses.  Out of these 100s of papers, guess which study gets cited as hard evidence by minimum wage proponents!  (Overall, the literature seems to indicate small job losses, by the way.)
2) Historically most changes in the US minimum wage have been modest, e.g. an increase from $2.65 in 1978 to $3.35 in 1981.  Some states and cities are now contemplating much larger changes, from the current $7.25 to $15.  It is quite possible that research done on small hikes does not translate into larger ones.  For instance, automation opportunities that McDonalds would ignore at a $1 increase may be too tempting to pass up at the President's proposed $3 increase. 
3) None of the minimum wage studies have been able to deal with long term consequences, such as how many McDonalds might end up closing or and how many never open because of higher labor costs.