The Shechitah Process

Intention to Shecht and Jewish Force

1. A valid shechitah must be caused by the applied force (Kocho) of a valid shochet, but not necessarily with his intent. For example, if a valid shochet throws a knife in a random direction and it ends up shechting an animal, that is kosher, but if the knife falls or even if a valid shochet intentionally drops the knife in a way that shechts the animal would not be kosher.
2. It remains undetermined whether or not a secondary force would be sufficient for shechita; therefore, throwing a rock and hit knife that then shechts an animal would be invalid.
3. The rebound force of a knife thrown against the wall that rebounds and shechts an animal is considered to be the applied force of the shochet and valid.
4. Shechitah by force of gravity alone is invalid. As such, an animal slaughtered by a knife thrown straight up that fall straight down with zero movement in the xy plane would not be kosher. If it did move to one side a little in the xy plane, then that would be kosher.
5. Nevertheless, some gedolei HaPoskim write that the shochet still needs some threshold of awareness. He can't be shechting in his sleep, tripping on things, or pushed by a goy. That would be invalid.
6. If a Jew pushes another Jew, we should be machmir that it's koach kocho and the second guy didn't have kavanna.
7. Some say shechitah done in a manner that starts off with the intention to be done in invalid way but ends up being done in the valid way is still invlaid.

Credibility & Dispute

1. If a dispute arises between the shochet and others regarding the kashrut of a shechita he did/they witnessed, there is much debate about the kashrut of the meat, depending on the circumstances, such as what the Shochet claims the issues were, if he made any excuses or made any marks on the animal, etc.

Shechting for a Different Religion

1. Shechting an animal with any idolotrous statement or intention is prohibited and renders the meat prohibited from benefit on a Torah level, regardless of whom it belongs to. If he shechted with a non-idolotrous but still non-Jewish intention, it is prohibited on a rabbinic level. For example, if he thinks that shechting the animal will magically cause his illness to be healed or in honor of an angel that ministers over the sun, moon, stars, or mountains.
2. Practically speaking, this issue is most relevant in Muslim slaughterhouses where the administration requires all slaughter be done facing Mecca and preceded with a declaration of the Takbir ("Allahu Akbar..."). If the Muslim standing next to the Jewish shochet is the one saying it, strictly speaking there is no issue, but it is still praiseworthy to stop this practice.