Originally a man could divorce his wife without her consent but about a thousand years ago Rabbi Gershom made a near universally accepted decree that she must consent to the divorce. The 100 Rabbi Excemption just allows him to divorce her the old way. The woman does not need an agent to accept the get for her. (The physical delivery of the document may still need to be effected)
Suppose the husband has really good insurance and the wife will lose this if divorced. Anyone could raise this issue to a Rabbi the man approaches and the Rabbi could decide not to endorse the petition.
In practice, because thelaws of divorce are treacherous waters, i is far safer for the man to take on a second wife which can also achieved with the 100 Rabbi Exemption.
There are some laws regarding the production and delivery of the document but a single scribe is capable of creating the document with the husband and two kosher witnesses.
A beit din would provide the mediation service to work out matters such as child support and division of assets but their factfinding and due diligence responsibilities are not codified as a spiritual matter. A rabbi serving on the beit din could consider any testimony or evidence that he believes to be credible.
The rabbinical organizations such as the Rabbinical Council of America or the Chief Rabbinate, however, will probably refuse to regonize the Gittin of a rabbi who has demonstrated that he is a complete bonehead by being negligent in these matters. Whether the get of a bonehead rabbi is valid, post facto, is a massive problem for jewry.