If while one was doing the shechitah the knife fell from his hand, and then he picked it up and completed the shechitah, it is valid – if the pause was no longer than what it takes to make a shechitah. The same applies to a case where he had to sharpen the knife, or where he grew weak while doing the shechitah, and his companion finished it for him. Rabbi Shimon says, the pause should not be longer than what it takes to examine the knife.
If in doing the shechitah one properly severed the trachea, but tore the esophagus with a nicked knife, then Rabbi Yesheivav says that the animal becomes a nevelah – not slaughtered at all – and therefore carries ritual impurity. Rabbi Akiva says that the animal becomes a trefah: it is slaughtered, but considered to have an internal defect that would cause it to die within a year. Trefah cannot be eaten, but it does not carry ritual impurity.
Rabbi Yesheivav stated a rule: any animal that became unfit through slaughter becomes a nevelah, but if another incidental defect caused it to become unfit, it becomes trefah, and subsequently Rabbi Akiva agreed to it.
Art: Gerard Terborch - Woman Washing Hands