Hopefully, this will spur your thoughts as to the issues that you should consider when you are selecting a mediator as well. It also could help you try to imagine what mediator your opponent is looking for -- and that may be the person who gets a tough case resolved.
Another question for debate and discussion: are there other characteristics that you look for in selecting a mediator that are not on here? If so, what are those characteristics? Why do you look for them?