A new mishnah! In the case of a knife fell and slaughtered the animal officially correctly, the shechitah is not actually kosher because a person must be involved doing the slaughtering. But if a person dropped the knife, even without intent, then the person is there as an agent, and the shechitah may well be kosher. The question is whether intent is required for shechitah to be valid. Also, the case of produce that falls into a channel of water, and the produce is removed by a person who has impure hands - but the process itself will purify his hands. The water is one of 7 liquids that, when in contact with produce, makes the produce susceptible to impurity. Plus, the levels of purity and impurity - and how immersion in the mikveh to be purified requires intent for the required level of purity to follow - for example, to eat ma'aser sheni food. Which seems to require more planning than we might have thought.