Although I've mediated a variety of disputes (elder, business, landlord-tenant) most of my work is in divorce mediation. The six attributes Robert Angyal lists in this article are essential in helping couples come to their best agreement during a divorce.
As Robert writes, in order to ensure that potential mediators possess all these attributes, you shouldn't be shy about interviewing them. If they don't understand what you are talking about, you shouldn't retain them. You will be doing yourself a disservice if you choose a mediator who lacks any of these attributes - because they won't get the most effective mediator possible.