Gemara

Rav Papa: If there is excrement in its place (the anus), one may not read Shma.

Question: What is the case?

If it is visible, this is obvious!

If it is not visible, this is unreasonable - people are not (able to clean themselves absolutely to be like) angels!

Answer: The case is, if it is visible when he sits, but not when he stands.

Question: Why is this different than excrement on his body?

Rav Huna: (Even) if excrement is on one's body, or if his hand is inside a Beis ha'Kisei, he may say Shma;

Rav Chisda: He may not say Shma.

Answer: It is filthier in its place.

Berachos 25a - Rava: Rav Huna learns from "Kol ha'Neshamah Tehalel Kah" (the nose and mouth, which are used for Neshimah (breathing) praise Hash-m. we are not concerned for the cleanliness of the rest of the body.) Rav Chisda learns from "Kol Atzmosai Tomarnah Hash-m Mi Chamocha" (all the limbs praise Hash-m).

Rishonim

Rif (Berachos 16a): If excrement is on one's body, or if one's hand was dirty from a Beis ha'Kisei, Rav Huna permits to say Shma and Rav Chisda forbids.

The Halachah follows Rav Huna. Firstly, he was Rav Chisda's Rebbi. And secondly, in Yoma we answer to show how Rav Papa can hold like Rav Huna. This shows that the Halachah follows Rav Huna.

Ba'al ha'Ma'or: The excrement on the body is b'Makom Kinu'ach (where one cleans himself) or in a similarly covered place where it does not emit a smell and it is not prone to become exposed. If it was in an exposed place, it would not be more lenient than excrement on one's sandal, which was an unresolved question! . Rav Hai Gaon rules like Rav Chisda, for the Halachah follows Rav Chisda regarding an odor emanating from a source (one must distance four Amos from where it can be smelled). All the more so it is forbidden when excrement is on his body!

Rebuttal (Hasagos ha'Ra'avad): Rav Chisda cannot discuss excrement b'Makom Kinu'ach! If it is not prone to become exposed, it is not a problem, for people are not angels (Yoma 30a). Rav Chisda cannot argue with this! If it is prone to become exposed, Rav Papa forbids this! Rather, it is elsewhere on the body, which is not so filthy. It has a smell, but we discuss when one does not smell it because it is covered by garments. The Halachah follows Rav Huna, like the Rif explained. It is unlike excrement on one's sandal, which becomes exposed when one lifts his leg. It is unlike an odor emanating from a source, since it is covered. Rather, it is like an odor without a source.

Ba'al ha'Ma'or: Regarding one who put his hand in a Beis ha'Kisei, we must say that a wall separates his body from the Beis ha'Kisei, for one may not read Shma opposite a (used) Beis ha'Kisei, even if it is now clean. The Rif's text (his hand was dirty from a Beis ha'Kisei) is unlike all Seforim of our region.

Hasagos ha'Ra'avad: The Rif cannot mean that his hands are filthy. Surely, one would need to wash them for Shma!

Milchamos Hash-m: Sifrei Sefard say 'his hand was dirty from a Beis ha'Kisei', i.e. from the rocks used to clean oneself. There is no excrement on his hand, but it is repulsive and one would not eat without cleaning it. "Kol ha'Neshamah Tehalel Kah" is fulfilled, for the eyes and heart do not see excrement. "Kol Atzmosai..." is not fulfilled, for his hand is not fit to praise Hash-m.

R. Yonah (DH Itmar): The excrement on his body is covered by garments. Rav Huna permits just like one may say Shma within four Amos of covered excrement, since it cannot be smelled; Rav Chisda requires the entire body to be clean and in a clean place. Some say that Rav Huna requires the excrement to be in a place where it is naturally covered by the body without garments, e.g. under the arm. The Gemara in Yoma supports this. It discusses excrement in its place on a clothed person. It says that if it is visible, i.e. in a place where it would be visible if he were naked, he may not read.

Rambam (Hilchos Kri'as Shma 3:11): If there was a smudge of excrement on his body or his hands were dirty from Beis ha'Kisei and there is no odor from them because the filth is so small or dry, one may read Shma.

Question (R. Yonah, ibid. DH veha'Rif): The Rif and Rambam do not require the excrement to be covered by garments, it can even be on his hands. How can he see it at the time of Shma?! One must distance four Amos from excrement, even if it is as hard as earthenware, dry, and has no odor!

Suggestion: The Rambam says that there is only a smudge to answer this, i.e. it is so small and dry that it is not considered excrement.

Rejection: The Gemara says that the argument is based on "Kol ha'Neshamah..." and "Kol Atzmosai..."!

Rambam (ibid.) If the excrement was in its place, even if it is visible only when he sits but not when he stands, he may not read until cleaning it well because it is moist and has an odor. Many Ge'onim forbid when it is on his body; it is proper to be stringent.

Kesef Mishneh: The Rambam explains that it is filthier in its place for then it is always moist and odorous

Rosh (Berachos 3:45): Rav Huna and Rav Chisda argue about when excrement is on one's body but covered by garments, or if his hand was in a Beis ha'Kisei, i.e. he stuck it through a hole in the wall and he does not smell anything foul. , Rav Huna permits to say Shma and Rav Chisda forbids. Even though Rav Chisda was Rav Huna's Talmid, R. Chananel rules like Rav Chisda for he is stringent. Presumably, the Halachah follows Rav Huna because the Gemara answers that Rav Papa can agree with him (Rif). Some say that Rav Huna requires the excrement to be in a place where the body itself covers it; the Gemara supports this. The text of the Rif and Rambam permits when excrement is on his hands. This is unreasonable.

Poskim

Shulchan Aruch (OC 76:4): If there is excrement on one's body but covered by garments, or if he stuck his hand through a hole in the wall around a Beis ha'Kisei and he does not smell anything foul, some permit to say Shma and some forbid.

Question: When saying Shma (or any Divrei Kedushah) we require "V'Hayah Machanecha Kodesh"!

Answer (Rashba 25a DH Tzo'eh): Since it is odorless, even if it is moist it is like dirt from sweat. Since it is covered, this is considered Machanecha Kodesh.

Question: This implies that if excrement is on his garment and covered by other garments, all permit. Why is this different than excrement on one's shoe, which is forbidden (76:2)?

Answer #1 (Magen Avraham 6): Other garments are not Batel to a person, but a shoe can be Batel (Rosh Berachos 3:51).

Answer #2 (Hasagos ha'Ra'avad): A sandal becomes exposed when one lifts his leg.

Mishnah Berurah (12): Even though all permit excrement on his garment if it is covered by other garments, one should be careful that all his garments be clean, especially at the time of prayer.

Kaf ha'Chayim (15): Early Chasidim were particular not to have even a drop of urine on their garments.

Mishnah Berurah (10): One may say Shma facing such a smudge, for it is not considered excrement, rather, like dirt from sweat. However, one may not read Shma if his own hands are dirty from dirt of sweat or from scratching the head. One must clean them. Water is not Me'akev.

Question (Eshel Avraham 5): It is not clear if the Shi'ur for a garment to cover it is three (by three) fingers or three Tefachim.

Rebuttal (Bi'ur Halachah DH u'Mechusah): It does not matter what covers it. Even thick spit can cover it (76:6)!

Shulchan Aruch (ibid.): Some say that the lenient opinion requires the excrement to be in a place where it is covered (by the body) without garments; e.g. under the arm.

Mishnah Berurah (13): Additionally, there must be a garment over the area.

Shulchan Aruch (ibid.) It is proper to follow the stringent opinion.

Mishnah Berurah (12,14): Just like the stringent opinion requires all the limbs to be clean, they may not be within four Amos of excrement. In pressed circumstances one may rely on the lenient opinion that requires only the mouth and nose to be clean.

Rema: The law of semen on the body is the same as that of excrement.

Magen Avraham (7, according to Machatzis ha'Shekel): If semen is on his garment and it is covered by other garments, all permit. We learn from Shabbos 114a (if a stain of semen is found on a Chacham's garment, he is Chayav Misah bi'Dei Shamayim for disgracing Torah in the eyes of people. We are not concerned for learning or praying while wearing it!) If semen is on his skin and covered by garments, it is permitted (like excrement) according to the first opinion. We learn from one who saw Keri on Yom Kipur. Hagahos Maimoniyos (Hilchos Shevisas Asor 3:6) permits one who normally washes off the semen to do so on Yom Kipur. Rashi (Yoma 88a DH ul'Erev) says that he washes so it will not be a Chatzitzah regarding Tevilah. They do not require washing it to permit learning or praying!

Gra (DH v'Shichvas): Sukah 26b connotes that one may wear Tefilin even at the time of an emission! (R. Yosi always requires youths to remove Tefilin before sleeping. Rashi explains that the Gemara thought that he forbids a Ba'al Keri to wear Tefilin, i.e. perhaps he is prone to see Keri while asleep. Abaye rejects this; rather, it is forbidden when his wife is with him, we are concerned lest he have relations while wearing Tefilin.)

Note: Abaye says that (perhaps) R. Yosi does not forbid to wear Tefilin lest one see Keri at the time. It is not clear how this shows that he permits at the time of an emission.

Magen Avraham (ibid.): However, Sefer Chasidim forbids even if semen is on his garment.

Mishnah Berurah (15): One should clean or change the garment so the Tum'ah not cling to him, especially if it was Keri, so it will not be a reminder of his mishap.

Kaf ha'Chayim (21): It is a stringency to consider semen like excrement.

Shulchan Aruch (5): If there is excrement on the anus, all forbid to read Shma.

Kaf ha'Chayim (27): One should be careful to clean himself very well after eliminating. Nothing cleans as well as water.

Karyana d'Igreta (1:373, 374, based on Divrei Chayim 2:9): One need not be paranoid to clean repeatedly until the toilet paper is clean. Chazal permitted a person only three rocks with which to clean oneself on Shabbos (Shabbos 81a). Granted, people used to be skilled at this. Nevertheless, it suffices to wipe five or six times with toilet paper and then with a little water. One gets as clean as people did in the days of Chazal. One must not leave the area wet for medical reasons.