Rabbi Broyde has a typically excellect summary of the subject on the Hirhurim blog. Subject discussed on this blog I II III
Some Final Observations Now That the Summary is Over
It seems to me [and to preempt any questions, I am speaking just for myself and for no organization that I am involved in: neither Emory University nor its law school, nor its law and religion program, nor the Beth Din of America nor the Young Israel where I am the Founding Rabbi necessarily agree with my thoughts] that given since this dispute is without clear precedent, one can say for certain that as a matter of halachic policy it is a bad idea to allow a convert to serve on a bet din.
The rationale for this seems clear. Given the fact that there are many, many eminent poskim who think such a conversion is invalid even bedieved, it would be a terrible disservice to any convert to intentionally staff their conversion panel with such a rabbi. It makes such a conversion invalid according to many poskim for no good reason. An indisputably valid panel is a wise idea in every case and for every convert lechatchila. (This is even more so true in this matter where a hachra’ah based on logical rules seems so hard.)
The intentional decision to place a rabbi who is a convert on a conversion panel is nearly a form of rabbinic malpractice in my view; since so many competent and qualified rabbis are present in our times, why staff a rabbinical court with one whose qualifications are to be questioned as a matter of halacha?