There is one key point in the broadcast Ask JTF for October 26, 2014 that I have to disagree with.
I don't think we should be more lenient in accepting as converts, when the father is Jewish but the mother is not, than when the non-jew has 2 non Jewish parents.
In the Biblical book of Ezra when Ezra was faced with such situations, he did not look for easy conversions as a solution for mixed marriages or children of mixed marriages.
Our rabbis taught that the sin of the Golden Calf happened because of the incitement of the Erev Rav, the insincere converts that Moshe (Moses) accepted when the Jews left Egypt.