NEJ s.v. Goren, Shlomo
"Shortly after his election he was involved in a violent controversy stemming from the unconventional manner in which he solved the problem of a brother and sister who had been declared mamzerim by the rabbinical courts, including the Bet Din of Appeals."
Rav Goren relied (in part) on the view of the Rambam that in a conversion for the sake of marriage if the convert resumes his previous non-halachic behaviour then the conversion is nullified. Since A non-jew cannot have the status of mamzer the problem was solved. One of the major complaints against was the claim that this view of the Rambam only applies if the convert resumes his previous behaviour immediately after the conversion whereas in the case in question the convert had only resumed his previous behaviour after a significant amount of time had passed.
Rav Goren's position would seem to be validated by the arch-enemy of the Chief Rabbinate- the Satmar Rov (see for example Divrei Yoel 131). In Divrei Yoel 90 (I will try to provide an exact quote later) he writes that he believes that the coversion mioght be rendered invalid even if the convert is "Chozer L'Suro - L'BaSof" implying that even if time passes the conversion could still be nullified.