Gemara

(Rava): One should accustom his wife to rinse inside folds of skin with water.

Question (Beraisa): Water need not enter folds of skin or Beis ha'Starim (places normally covered by other parts of the body).

Answer: Indeed, water need not enter them, but they must be (free of Chatzitzos,) so that water could enter, like R. Zeira's law;

(R. Zeira): If (the flour and oil of) a Minchah could have been mixed, mixing it is not Me'akev. If it could not have been mixed (for there was too much flour), mixing is Me'akev.

(Ravin): Once, a Shifchah of Rebbi's house found a bone between her teeth after immersing. Rebbi made her immerse again.

67a (R. Yochanan): If she opened her eyes too much or closed them too tightly, the immersion was invalid. (This is a Chatzitzah above or below the eye, respectively.)

(Reish Lakish): A woman immerses in her normal standing posture, like the way we inspect Tzara'as:

(Mishnah): When inspecting Tzara'as (in the underarm or near the Ervah), a man poses as if he is picking olives or hoeing. (If the Nega cannot be seen, he is Tahor);

A woman poses as if she is weaving or nursing.

Chulin 10a (Beraisa): If a Tamei immersed, and later found a Chatzitzah on his body, even if he was working the whole day (after Tevilah) with that substance (of the Chatzitzah), the Tevilah is invalid, unless he is sure that there was no Chatzitzah when he immersed.

Since he was known to be Tamei, we leave him in his Chazakah.

Rishonim

Rambam (Hilchos Mikva'os 2:13): If (at the time of Tevilah) a Nidah put her hair in her mouth, or clenched her hand or lips, or (later) found a bone between her teeth, it is as if she did not immerse.

Rosh (Hilchos Mikva'os (b'Sof Nidah) 35): Reish Lakish teaches that a woman need not spread her thighs or lift her arms excessively, rather, like normal. She should not open her eyes too wide or close them too tightly, or clench her mouth. She should spread her thighs and lift her arms like when walking. She must clean her teeth so there will be no Chatzitzah there.

Ba'alei ha'Nefesh (Sha'ar ha'Tevilah Siman 2, cited in Beis Yosef YD 198 DH Kosav ha'Ra'avad): Rebbi disqualified his Shifchah's Tevilah only because she found a bone. She had not checked her teeth beforehand, and even so the Tevilah was invalid only because she found a Chatzitzah. This is unlike checking the body and shampooing the hair. We learn from this that she must check her teeth for a bone or meat or something else pressed inside. If she did not check her teeth or Beis ha'Setarim, and not after immersing, until she ate or engaged in Kesamim or food and later checked and found a bone or Chatzitzah in her folds, presumably we are lenient and say that the Chatzitzah arose after Tevilah, since the water need not enter there.

Beis Yosef (ibid.): The Tur brought this in Siman 199.

Poskim

Shulchan Aruch (YD 198:25): If she did not rinse Beis ha'Setarim and inside folds, and a Chatzitzah was found there, the Tevilah was invalid. If no Chatzitzah was found there, even though she did not check beforehand, the Tevilah was valid. This is unlike checking the body and shampooing the hair.

Shach (32): The Levush (25) and Divrei Chamudos (92, on Rosh Hilchos Mikva'os 25) wrote that since in Beis ha'Setarim there is room to remain there and stick to her folds, we say that surely it was not there. If so, why would it fall after Tevilah? There was no need to say so. It is unlike checking the body and shampooing the hair, for the water must go there, so we attribute stringently (and say that the Chatzitzah was there at the time of Tevilah). Here, the water need not reach there (we need only that water could reach there), therefore we attribute leniently, like in Saif 26. The Ra'avad connotes like this, and the Tur and Shulchan Aruch below (199:9).

R. Akiva Eiger: If we need a proof (that the Chatzitzah came later), in Sa'if 26 there is no proof to be lenient, for a Chatzitzah was found. The Shach concludes that we attribute leniently, but we must check Beis ha'Setarim, just checking after Tevilah helps. We are not concerned lest it fell after leaving the water. We can ask from Sa'if 26, in which she did not check Beis ha'Setarim, for she found a Chatzitzah, just we can attribute it to what she engaged with! This requires investigation.

Pischei Teshuvah (16): Noda bi'Yehudah (YD 64)) discusses a woman with a wax ring in her Pruzdor for medical reasons. He said that surely we say that she is particular about it, so it is a Chatzitzah. It gets dirty whenever she sees Dam Nidah, and she must remove it to clean it for a Hefsek Taharah or birth. Perhaps it interrupts checking during the seven clean days, and she must remove it. However, even though Chachamim said that water must be able to enter Beis ha'Setarim, it need not be able to enter what is Balu'a (enveloped). If the ring is so far in that the Ever does not reach there during Bi'ah, it is Balu'a, and water need not be able to enter there, so she need not remove it for Tevilah. The Chasam Sofer (192) said that we do not say that she is particular about it just because she must remove it for birth. This is not due to concern for it or for dirt, rather, to clear place for the baby! A man's ring without a stone is not a Chatzitzah, even though he removes it when wearing Tefilin or taking the Lulav. However, if she must remove it for a Hefsek Taharah, this is called Hakpadah. If we are unsure how deep inside it is, even though perhaps this is a Safek due to lack of knowledge, for a knowledgeable woman could know, since it is dangerous (causes her) great weakness to remove it, this is a Chatzitzah on the minority that she is not particular about, so we can be lenient.

Pischei Teshuvah (16): Noda bi'Yehudah (2 YD 135) says that a Rav wanted to distinguish within Beis ha'Setarim. Places where water could reach by itself, e.g. in the mouth if it were open, or openings of the nose and ears, the Torah revealed that water need not go there, but it must be able for water to get there. However, regarding her Ervah, even Beis ha'Chitzon, even if she spread her legs, only a little water would enter the beginning of the place. Therefore, further in from what is seen when a girl sits, we do not require that water could get there. The Noda bi'Yehudah refuted the Rav's proofs. (Also the Rema in Sa'if 43 is unlike him.) Shevus Yakov (1:69) says that regarding a minority that she is particular about, we are lenient about the Safek, for it is mid'Rabanan. (This requires investigation, for we are not lenient against Chezkas Isur. Here there is Chezkas Tum'as Nidah! He must hold like the Pri Chodosh (who disagrees), but I wrote that the Halachah does not follow the Pri Chodosh.) Also, since she says that it is mortally dangerous to remove the ring, and she does so only when forced to for birth, this is called that she is not particular. Also R. Akiva Eiger and the Gaon from Lisa said that it is not a Chatzitzah.

Shulchan Aruch (YD 198:26): If she did not clean between her teeth or Beis ha'Setarim before Tevilah, and not afterwards, until she engaged in Kesamim and food, and she found a bone between her teeth or a Chatzitzah between her folds, we attribute leniently and say that it came after Tevilah.

Shach (33): The Roke'ach disagrees. If a Tamei immersed, and later found a Chatzitzah, even if he was working the whole day with that substance, the Tevilah is invalid (Chulin 10a). One should be stringent.

Machatzis ha'Shekel (DH v'Yesh): Regarding one who did not check before or after Tevilah (Sa'if 25), the Shach said that we are lenient about a place where water need not go. The Roke'ach is not more lenient about such places, so one should be stringent also there.

Question (Gra 199:27 and R. Akiva Eiger on Shach): This leniency (of the Shulchan Aruch) requires investigation.

Beis Lechem Yehudah (16): L'Chatchilah, we are stringent. B'Di'eved, she is permitted. If the night passed, she need not immerse.

Shulchan Aruch (198:8): If she did not look at the rest of her body (other than her hair), the Tevilah was invalid, for the Torah requires looking at the rest of her body.

Shulchan Aruch (9): This refers to the rest of her body. Water need not enter Beis ha'Setarim, therefore if she did not look at it and afterwards she looked and did not find anything, the Tevilah was valid.