Mishnah 6 discusses four more blemishes on the face and head: on the nose, on the lip, and in the teeth.
The Nose:
The Mishnah states: "Chutmo shenikav, shenifgam, shenisdak" - the nose of the cow, goat, or sheep was punctured, a piece is missing from it, or it was slit even though nothing is missing. These three are considered permanent blemishes, because they do not heal on their own and they are visible from the outside. A practical difference emerges from this: a puncture on the inside of the nose, or a piece missing from the inside, are not a blemish, since they are not visible from the outside.
The Lip:
Similarly, "sfato shenikvah, shenifgemah, shenisdekah" - its lip was punctured, a slice was removed from it, or it was slit as if with scissors, in a way that no flesh is missing but it is divided into two pieces. These too are blemishes that will not heal, and therefore it is permitted to slaughter such an animal.
The Dental System in a Cud-Chewing Animal:
The dental system of a cud-chewing animal - a cow, goat, or sheep - has an unusual structure. In the front of the mouth, only on the lower jaw, there are eight incisors. On the upper jaw there are no incisors at all, only a flat surface. The animal grasps the grass with its lower teeth, plucks it, and grinds it, while the chewing, including the chewing of the cud, is done with the back teeth.
Deeper in the mouth, for lack of a more precise term, there is a second set of teeth: the premolars and molars, like those back teeth in a person's mouth. There are twenty-four of them, divided equally:
Six on the lower jaw on the left side.
Six on the lower jaw on the right side.
Six on the upper jaw on the left side.
Six on the upper jaw on the right side.
Altogether, there are thirty-two teeth, the same number as a person's teeth. The front ones are called premolars, and the back ones, deeper toward the throat, are called molars. In the language of the Mishnah, these are called 'inner', as opposed to the 'outer', which are the eight incisors. It seems that the Mishnah distinguishes within the inner teeth themselves between the 'meta'imot' - apparently the front premolars - and the teeth deeper than them.
The Mishnah's Law Regarding Teeth:
The Mishnah states: "Chitav hachitzonot shenifgemu o shenigmemu" - these are the ones visible when the animal opens its mouth. If one of the eight front teeth is broken, or the incisors are worn down until they become like flat stumps, this is a blemish. But "hapenimiyot shene'ekru" - the twenty-four inner teeth are not considered a blemish unless they are completely uprooted. A break in an inner tooth, or a worn-down molar, is not a blemish; only a complete uprooting is considered a blemish, because it can be noticed when the cow, goat, or sheep opens its mouth, and as the Gemara explains, this is a blemish visible from the outside.
The Opinion of Rabbi Chanina ben Antigonus:
Rabbi Chanina ben Antigonus disagrees and says: "Ein bodkin min hamasimos velifnim, ve'af lo es hamasimos" - meaning, the inner teeth are not considered at all, since they are not included in what is visible from the outside, and therefore it makes no difference what happens to them. All twenty-four of these teeth do not disqualify the animal: whether one of them is missing or all of them are missing, it is not a blemish, because it is not visible from the outside. However, the halachah does not follow his opinion.
In summary: In this Mishnah we learned four blemishes of the face and head - in the nose, the lip, and the teeth. The general rule emerging from all of them is twofold: the blemish must be permanent, not expected to heal, and it must be visible from the outside. Therefore, defects in the inside of the nose are not a blemish; regarding the outer teeth, a notch or abrasion is sufficient to be considered a blemish; and regarding the inner teeth, it is only a blemish if there is a complete extraction, which is visible when the mouth is opened. According to Rabbi Chanina ben Antigonus, the inner teeth do not disqualify the animal at all, but the halachah does not follow his opinion.