Levítico 21:7 Halajá: Mishneh Torah, Marriage, Gray Matter I, Mishneh Torah, Prayer and the Priestly Blessing & Shulchan Arukh, Even HaEzer

Intercourse prohibitions according to the Torah for which there is no punishment of karet are called “negative prohibitions”. They are also called “holy prohibitions”. There are nine [such prohibitions] and they are: a widow to a high priest, a divorced woman or zona or ḥalala to a high priest or to an ordinary priest, a mamzeret to an Israelite man, an Israelite woman to a mamzer, an Israelite woman to an Ammonite or Moabite man, an Israelite woman to one with crushed [genitals], or severed [genitals], one’s ex-wife after she has remarried, one’s yevama who married a stranger while still under the yavam’s control. A ḥalutza is like a divorced woman and is forbidden to a priest according to Rabbinic law. The Gibeonites are like mamzerim, whether male or female, and they are prohibited according to Rabbinic law. The Gibeonites will be explained in the Laws of Forbidden Intercourse.

Another major problem exists with implementing hafka'at kiddushin today. The Gemara records many objectionable marriages that are binding, indicating that the Rabbis do not annul them. For example, Chazal do not annul the marriage of a kohein and a divorcee, although such a marriage is explicitly prohibited by the Torah (Vayikra 21:7).⁴See Teshuvot Binyamin Ze'ev (106) for a list of objectionable marriages where Chazal do not invoke hafka'at kiddushin. While criteria presumably exist to determine when marriages may be annulled, the Gemara never articulates them. The Rashba (Ketubot 3a) provides some insight:

Uncleanliness of the hands: A priest who has not washed his hands must not perform this rite. But he first washes his hands as far as the wrists, just as the priests did in preparation for the Temple service and then he blesses the people, as it is said, "Lift up your hands to the sanctuary",^*That is, wash your hands for a holy service. (Psalms 134:2). The profaned^*Who himself, or whose father prior to his birth, has violated the restrictions on the priests in marital relations. priest does not perform this rite because he has not the status of priesthood.