Seif 1

The shechita of an `oved kokhavim/ idolater is nevelah [a not-kosher-shechted carcass], even if he's a minor, and even if he does not perform idolatry (e.g. a ger toshav), and even if others watch him.

Seif 2

A mumar/ wanton sinner who eats nevelot deliberately, a Yisrael can check the knife and give him it, then it's permitted to eat from his shechita, even if he shechts just for himself. Provided he knows the laws of shechita. But if he did not check for him the knife initially, it's forbidden to eat of his shechitah until he checks it afterwards. And he should not be given to shecht initially even with a kosher person standing over him without checking [the knife] for him [but just relying that] the knife is kosher based on checking it afterwards.

Rema: Whoever shechted and a treifah once came out from under his hand, if that's not muchzak/ an established pattern then it's permitted to eat from his later shechitah. However, this is determined by the dayan/ judge's eyes' view of the man shechting. If he's already faulty and accustomed to do this we remove him. (MHRI"Q Shoresh L"G)

Seif 3

A wanton sinner who shechted, even if he swore that he shechted with a good knife he's not believed.

Seif 4

A wanton sinner who shechted alone for himself, and he has with him a good knife and a not good one, and says that he shechted with the good one, he's believed. And even if the meat is [already] in his hand, if there are experts in the city he is believed in saying an expert shechted it for me.

Seif 5

A mumar l'hakh`is [one who transgresses out of spite] even in regard to one mitzvah, or who is a mumar to idolatry, or profaning Shabbat publicly, or who is mumar lekhol-hatorah [transgresses the entire Torah] even with the exception of two [mitzvot], has the status of an `oved kokhavim [idolater]. (R' Yerucham)

Rema: And one who doesn't consider shechita and eats nevelot without teyavon [craving or convenience] even though he's not doing it in spite, he has the same status as a mumar l'hakh`is. (So concludes B"Y from Rosh's words)

Seif 6

A mumar in some other transgression, it's unnecessary to check the knife for him. Rambam says one must, but that's if he's mumar due to the transgression. However, one who is an invalidated witness due to a transgression in the Torah prohibitions, it's unnecessary to check the knife for him even according to Rambam. (B"Y and ShKh"Kh of Rambam)

Rema: However if he's an invalidated witness because he eats nevelot even though he's not mumar in this, since he's suspected of eating nevelot he has the rule of a mumar for this. (so reason the B"Y and Rambam)

Seif 7

A mumar in `orlot [foreskin], his rule is as a mumar in one transgression. And if he's only `arel because his brothers died from circumcision, he's kosher like other Yisrael.

Seif 8

A Cuthite, even today, his rule is like an idolater.

Seif 9

A Saducee or Boethusian (followers of Zadok and Boethus who were among the students of Antigonus of Sokho, who went out to tarbut ra`ah/ bad culture and deny the Oral Torah), their shechita is forbidden, unless they shechted while others were standing behind them and [others] also checked their knives.

Rema: A moser (informer), his rule is like a mumar and his shechita is invalid, but some permit it (B"Y #119 in the name of Rabsha), and see below, #119.

Seif 10

An invalidated person began the shechting and a kosher person finished, or a kosher person finished and an invalidated person finished, it's invalid. This applies when the invalidated person started in a thing that makes it nevelah for example veshet/esophagus or most of the kaneh/windpipe. But if the invalidated person began in [up to] half the kaneh and a kosher person finished it's kosher.

Seif 11

A Yisrael and an invalidated person were gripping the knife and shechting, it's invalid. Needless to say if each was holding a knife in his hand.

(Shechita of a monkey is invalid) (A"Z and it's in Tosefta at start of Chullin)