I will admit that I am not entirely comfortable with the idea of the mediator as a neutral. I prefer to think of the mediator as an advocate for each side in turn. Sometimes I feel that my role is to coach each side into negotiating the best deal they can get. Sometimes I try to persuade each side of the strengths of the other side's position. And sometimes I act as the advocate for agreement as opposed to the drawbacks of continued conflict. In none of these roles do I feel strictly neutral.
I also think parties need not choose a mediator who is strictly neutral in the sense of having no connections to either party, or in terms of having a more defense-oriented or plaintiff-oriented background. Parties might even prefer a mediator who seems disposed toward the other side's point of view because the other side is more likely to listen to that mediator. The important thing is that the parties--and the mediator--are aware of potential biases, because it may not be possible to avoid them. The mediator needs to persuade each side that he can be effective despite, or perhaps even because of, his own biases.
If the mediator cannot do that, lack of neutrality can be fatal to the success of a mediation. Witness what happened in Libya this week. A delegation from the African Union, including several heads of state, went first to Tripoli where they appeared to have persuaded Qadaffi to agree to a cease-fire and a road map toward a more democratic government. Then they traveled to Benghazi, where the rebels immediately rejected the deal, stating that no agreement in which Qadaffi remains in power would be acceptable. One reason this proposal may have been shot down so quickly is that the mediators lacked credibility with the rebels. The rebels know that these other African heads of state have been close to Qadaffi in the past, and they may be suspicious of any deal they propose, even though this deal may represent substantial progress, and even though it may be better than the status quo. To maintain credibility these mediators needed to distance themselves from Qadaffi. Perhaps they also would have had more success had they chosen to visit the rebels first, instead of appearing as a delegation of Qadaffi's friends bringing Qadaffi's offer to them. Instead of acting as honest brokers, they may have appeared to be supporters of Qadaffi making a last ditch effort to keep him in power. Perhaps some form of negotiated resolution of this dispute will still succeed, but whatever mediators are involved now may have their work cut out for them to restore a semblance of neutrality to the process.