On a law practice website I share with a friend, we have an article about non-lawyers and inexperienced lawyers pretending they can mediate a divorce settlement - sure, they MIGHT be able to help the parties achieve a fair and cheap resolution of their issues, but if that happens it is by accident.
An essential part of the process is that each side knows his or her rights. These cases aren't about two businesspersons or two neighbors fighting over a contract or boundary dispute, it's about fundamental fairness between two people who owe each other about the highest duty known to the law: That, coupled with the ability of each to continue to function financially, to provide housing and food on their tables, plus some semblance of a normal standard of living. Half the process is ensuring that each party knows his or her rights, and the other half is getting them to be reasonable in assessing the alternatives.
Within the last month, I've had two prospective clients come see me who have been in the mediation process with unqualified mediators. In one case, two "housewives" with no semblance of training in law or mediation, have a website - they are giving the married partners their untrained version of family law, performing guideline calculations with no evidence they know what judges do with various financial issues, and when they are done they are preparing a marital settlement agreement, which is the unlawful practice of law.
In the other case, the parties have been before a trained therapist for more than 2 years, and have not a single written agreement to show for it. Has it lasted so long because they are progressing to a meaningful conclusion? No evidence of that, and the parties don't seem to be getting along well, either. Do they know anything about the law? Not much from what I could tell.
If your goal is to gain an advantage because you know more about your rights than your spouse, you may perceive it is to your advantage to drag him or her to an untrained person to mediate the divorce - on the other hand, you may be in for an expensive litigation battle when the other decides to set aside your divorce decree and require you to start over, or in anger abandons the process and proceeds to litigation.
Your choice of mediator should include only those with a substantial background in family law, and mediation training.