R. Akiva holds that a Kidushin with an Isur Lav is not valid.
A person who has relations with his former wife after she was married to someone else does not invalidate her to Kehunah. (1)
A Chalal invalidates a Bas Yisrael to Kehunah with Bi’ah even though it is a permitted relationship.
R. Yosi holds that a Mitzri Sheni does not invalidate a Bas Yisrael to Kehunah with Bi’ah. (2)
R. Shimon Ben Gamliel holds that a Ger Amoni or Moavi does not invalidate a girl to Kehunah with Bi’ah. (3)
A Bas Yisrael who was raped or seduced or was married to an insane person is not invalidated to Kehunah.
A Bas Kohen who is pregnant from an out of wedlock relationship with a Yisrael may not eat Terumah. (4)
A Bas Yisrael who is pregnant from an out of wedlock relationship with a Kohen may not eat Terumah until she gives birth. (5)
A woman who has a grandchild who is a non- Jewish servant is not regarded as the grandmother.
A woman who has a grandchild who is a Mamzer is regarded as the grandmother.
A Bas Kohen who was married to a Yisrael and has a grandchild who is a Kohen Gadol is invalidated from eating Terumah.
The wives of an insane person or a Katan are Patur from Chalitzah and Yibum.
If a Bas Kohen has an out if wedlock relationship with a Yisrael she may continue eating Terumah as long as she is not pregnant. (4)
If a Kohen gives a Get to his wife on condition that it will go into effect a second before he dies she is immediately forbidden to eat Terumah.
A Bas Kohen who is widowed from a Yisrael may immerse and eat Terumah immediately up until forty days after she was widowed. (5)
If a Bas Kohen who is widowed from a Yisrael continues to eat Terumah after forty days and it turns out that she was pregnant she must pay the Kohen. (6)
If an Arusah had relations with the Arus and she is pregnant, Rav says the child is a Mamzer and Shmuel says the child is a Shtuki (Safek Mamzer). (7)
An alternative version of the dispute between Rav and Shmuel is that the Arusah is pregnant and she did not have relations with the Arus.
A BIT MORE
1. Since this relationship was originally permitted it does not invalidate her to Kehunah.
2. Since the children of the Mitzri Sheni are kosher, because the Torah says that the third generation of a Mitzri may marry into Klal Yisrael, therefore a girl who has relations with the Mitzri Sheni is kosher to Kehunah.
3. Since the daughters of the Ger Amoni or Moavi may marry into Klal Yisrael, because the Torah says that only the males from Amoni and Moavi are prohibited and not the females, therefore the girl who has relations with the Ger Amoni or Moavi is kosher to Kehunah.
4. Once she gives birth she may eat Terumah since she has a child from a Kohen.
5. This is referring to a case in which her husband dies on the day of marriage. Up until forty days after the death of her husband she may eat Terumah even though she might be pregnant. The reason is because even if she is pregnant, for the first forty days of pregnancy the child is regarded as just a sac of water and does not prohibit her from eating Terumah.
6. Since she was pregnant she is not allowed to eat Terumah and thus she must pay the value of the Terumah plus an additional fifth to the Kohen.
7. Even if both the Arus and the Arusah admit that they had intimate relations the child is a definite Mamzer according to Rav. Rava says the child is only a definite Mamzer according to Rav if she is suspected of having relations with other people.