Gemara

2a (Mishnah): All (may) slaughter, and it is Kosher, except for a deaf-mute, lunatic or minor, lest he slaughter improperly;

If any of them slaughtered while others looked on, the Shechitah is Kosher.

Question: 'All slaughter' connotes l'Chatchilah. 'And the Shechitah is Kosher' connotes b'Di'eved!

3a - Answer #1 (Abaye): 'All slaughter', i.e. even Kusim. This is only if a Yisrael supervises, but not if the Yisrael goes in and out.

Objection (Rava - Mishnah): If one leaves a Nochri with wine, the Yisrael need not sit and guard it the whole time. If he goes in and out, this suffices.

Answer #2 (Rava): 'All slaughter', i.e. even a Kusi. This is only if a Yisrael goes in and out.

Answer #3 (Rav Ashi): 'All slaughter', i.e. even a Yisrael Mumar, i.e. he eats Neveilos for pleasure;

Rava taught that if one checks a knife, a Mumar may slaughter with it, and one may eat it.

If the knife was not checked, a Mumar may not slaughter. If he did, we must check the knife afterwards. One may eat it only if the knife is good.

Version #1 - Answer #4 (Ravina): 'All slaughter', i.e. anyone who knows the laws, even if he is not established (to have skilled hands and not to weary during the Shechitah);

We must know that he knows the laws. If not, he may not slaughter.

If we do not know whether he knows, and he slaughtered, we test him. It is permitted only if he knows the laws.

'Any of them who slaughtered while others looked on, the Shechitah is Kosher' refers to one about whom we are unsure whether he knows the laws.

Question: It suffices to test him. Why must others see the Shechitah?

Answer: The case is, he is not here to be tested.

Version #2 - Answer #4 (Ravina): 'All slaughter', i.e. anyone who is established (to have skilled hands...), even if we do not know whether he knows the laws;

The others did not learn like Ravina. In Version #1, he permits one to slaughter only if we know that he knows the laws. The others rely on the majority, i.e. most who slaughter know the laws.

Question: Why didn't Rava learn like Rav Ashi, that the Mishnah teaches Rava's law?

Answer: Indeed, he does! Rava addressed Abaye based on Abaye's reasoning. (If the Mishnah discusses a Kusi, he may slaughter if a Yisrael goes in and out.)

9a (Rav Yehudah): Any Shochet who does not know the laws of Shechitah, one may not eat from his Shechitah;

The laws (Pesulim of Shechitah) are: pausing; chopping the Simanim; inserting the knife between the Simanim and cutting; not completing the Shechitah in the ring of the windpipe in the Shechitah began; and uprooting one of the Simanim from its place.

Question: What is his Chidush? All of these are explicit in the Mishnah!

Answer: Even if we have seen him slaughter properly two or three times, we may not rely on his Shechitah;

Since he does not know the laws, perhaps he paused or chopped without realizing.

Rishonim

Rambam (Hilchos Shechitah 4:1): If a Yisrael does not know the five matters that invalidate Shechitah, or similar matters, if he slaughtered by himself, he or others one may not eat from it. It is close to Safek Neveilah. One who eats a k'Zayis of it is lashed mid'Rabanan.

Rambam (2): Even if one slaughtered properly in front of us properly four or five times, if he slaughtered alone, one may not eat from it, since he does not know things that disqualify. Perhaps he invalidated Shechitah and he does not know, e.g. he unintentionally paused or chopped or slaughtered with a dented knife or did similar matters.

Hagahos Maimoniyos (1, citing Semag): A Shochet need not know all distinctions of pausing and chopping in the minority of the Simanim, and such matters. When he has a Safek, he will be stringent. He must know that pauses join up, for this is very common.

Rosh (1:13): We asked what is Rav Yehudah's Chidush, because all the laws are explicit in the Mishnah. Surely, one who is not expert about them does not know to be careful about them! We answered that even if we saw him slaughter properly two or three times, we are concerned. Even if we ask him whether he did one of the Pesulim (e.g. pausing or chopping), and it is clear from his answer that he did not, we do not rely on him. Anything that one thinks that he need not be concerned for it, he is not aware of it.

Mordechai (754): The Yere'im explains that 'he does not know Hilchos Shechitah' means that he does not know the basic laws. If he knows the basic laws, even if he does not know all the fine points of the laws, it is Kosher. Also Chachamim have doubts about certain Halachos! However, he must know to pay attention to a difference in Shechitah, and to ask about what he is unsure about.

Hagahos Ashri: Rav Yehudah mentioned only five laws. R. Tam says that even if he knows only these that commonly arise, he need not know more. If he is unsure, he will ask. If he does not find someone to ask, he will be stringent. Even an ignoramus knows that we are stringent about a Torah Safek! The Ri says that he must know the matters we have a Safek about, whether pausings add up. This was not resolved, and it is common. He must know how to check the knife on flesh, fingernail and three directions, lest he slaughter with a dented knife.

Beis Yosef (YD 1 DH v'Zeh): It seems that also the Rambam requires that he know how to check the knife.

Tosfos (3b DH Mai): Why did the Gemara ask that Rava should establish the Mishnah to teach Rava's law? He does! On 17a, he says that the Mishnah says 'all' twice, and one of these includes a Mumar! Rather, we ask why he didn't establish the first 'all' to teach his teaching.

R. Akiva Eiger (1:162): The Rambam (4:14) and Shulchan Aruch (2:2) say that regarding a Mumar, we must know that he is an expert. What is the source that the majority of Mumrim are not experts?! Even if the Rambam reasons that this is so, the Rambam writes a new law only if it is explicit in the Sugya, or one is forced to say so. Also, the Gemara said that the others did not answer like Ravina, for they hold that most who slaughter are expert. Rav Ashi established the Mishnah to discuss a Mumar, even though it is difficult, for the Mishnah says 'all who slaughter.' Why didn't he explain the Mishnah more simply, that anyone may slaughter, even a Mumar, if we check a knife and give it to him. This is if we know that he is an expert. If he does not know, he may not slaughter. If he slaughtered, we check if he is an expert. Regarding this we say that for all of them, if he slaughtered and he is not here, it helps if others saw. Many Acharonim asked this.

R. Akiva Eiger: I say that Tosfos' question bothered the Rambam. We cannot understand Tosfos' answer at all. The Rosh asked why we rely on the majority who are expert. The minority who are not expert should join with the Chazakah that it was not slaughtered! He answered that only a tiny minority are not expert. If so, we can say that a majority of Mumrim are experts, but a regular minority are not, so this joins with the Chazakah. In Yevamos (119b), Rava holds that even Chachamim join a Chazakah to a minority. The Stam Gemara holds that only R. Meir says so. Rav Ashi arranged the Gemara. He holds that even for a Mumar, Chachamim do not join the minority to the Chazakah. We rely on the majority. The Halachah is that we join them. The Rambam holds that for a Mumar (to idolatry, that we - it seems that this should say 'we must' - PF) know that he is an expert, for if not we join the (regular) minority to the Chazakah.

Poskim

Shulchan Aruch (YD 1:2): A Shochet need not know all the fine points of the laws. Rather, if he says 'I was unsure about this' and asks about it, this is considered that he knows the laws, unless he permits something that is really forbidden.

Shach (9): This means that he says 'if this law came in front of me, I would be unsure and ask about it.'

Be'er Heitev (12, citing Beis Yakov 31, or 4) says that if he forbids something that is really permitted, even if he does not permit anything forbidden, we depose him.

Mishbetzos Zahav (7): The Shach (242, Hanahgos Hora'ah 9) says that he will come to do oppositely and permit what is Asur. The Yerushalmi says so. If Isur fell into one of two pots, one of which is Asur, we assume that it fell into the Isur (YD 111:1). If it is really Heter, his ruling can cause one to transgress!

Pischei Teshuvah (7): Beis Yakov was concerned lest he be Mekadesh a woman with the meat, and we will rule that she is single because we think that it is not worth a Perutah. Also Mishbetzos Zahav says that we depose him even if he did not forget, just he misjudged. They argue about one who forbids (Heter) mid'Rabanan. We ignore Kidushin with an Isur mid'Rabanan, but Minchas Yakov says that we do not assume that the Isur fell into a pot that is Asur mid'Rabanan. If one forbids mid'Oraisa what is truly Asur mid'Rabanan, Mishbetzos Zahav would depose him, but Beis Yakov would not. However, Minchas Yakov's colleagues disagreed with him. If so, all agree that we depose in the former case, but not in the latter.

Rema: We test him about laws of Shechitah in YD 23, and checking the knife, and checking the Simanim after Shechitah (YD 25).

Beis Yosef (DH Kasuv): Machazik ha'Bedek brings from Rav Amram Gaon that if a Shochet does not know the laws of Bedikah, one may not eat from what he checked. If others may not rely on him to eat, also he may not rely on himself. We should hit and lash those who slaughter or check for themselves, until they accept not to do so until they are proficient in all of Tanach, several chapters of Talmud, and know Hilchos Shechitah. Even if they know only lesions in the lungs, one may not eat what they slaughter or check until they are expert in all the Treifos that Chachamim listed. One who checks must know the 70 Treifos. If not, perhaps they will come to him, and he will not know. He will be liable for feeding Treifos to Yisrael.

Darchei Moshe (9): It suffices if he knows the common Treifos. He need not know more than one who slaughters. This is the custom. In our laws of Bedikos, only Treifos of the lungs are mentioned. The others do not depend on the one who checks. He need not check for them, therefore he need not be an expert about them. If a Safek Tereifah occurs, he will ask a Chacham.

Rema: If he slaughtered, and he is not here to test him, we check the Simanim to see whether the majority was slaughtered. Whatever we can check, we check.

Gra (15): This is like it says in Sa'if 1, that whenever it is possible (to check), we do not rely on the fact that most who slaughter are experts.

Rema: This refers to places where there is no custom to get a Kabalah (certification). In places where the custom is to get a Kabalah, e.g. Ashkenaz and places drawn after them, the custom is not to check after the Shochet at all.