From: Rabbi Akiva Eiger
To: Unknown recipient
Rabbi Akiva Eiger questions the source for invalidating shechitah performed with a fingernail attached to an animal, arguing that since animals are treated as movable property (not land), and since a person is compared to land, the Mishnah's ruling may refer only to the slaughterer's own fingernail. After analyzing the Gemara, Rashi, Tosfos, and the Rishonim, he finds no conclusive proof that an animal's fingernail invalidates shechitah, and concludes with tzarich iyun.
Source: Shu"t Rabbi Akiva Eiger §51