On the phrasing of everyone can slaughter, everywhere and when, and with anything that can do proper slaughter (for example, a shard of glass). The Gemara shifts the focus from the animal to the person during the slaughtering - to include the Samaritan and a sinner, for example. Plus, Shmuel's father sent a knife and a question about it to the sages in the land of Israel to determine the permissibility of using it for shechitah. Also, the concerns about notched knives and how we know to check such a knife from the Torah. Plus, the different ways of checking the knife, including the sage who tested it on his own tongue.