Commentary for Avodah Zarah 5:9

ואלו אסורים ואוסרין בכל שהוא – every place where they were mixed there, even one in one-thousand, forbids everything.

The following are prohibited and render prohibited by the smallest quantity:
[a cask of] yen nesekh;
an idolatrous object;
skins of animals which have holes over the heart;
an ox which has been sentenced to be stoned;
a heifer whose neck was broken;
birds brought as an offering by a leper;
the hair-offering of a nazirite;
the first born of a donkey;
meat cooked in milk;
the scapegoat;
and non-consecrated animals slaughtered in the Temple court. Behold these are prohibited and render prohibited by the smallest quantity.
This mishnah contains a list of things that are prohibited and if even the smallest quantity of them is mixed up with a similar looking permitted item, the entire mixture is forbidden. The difference between this mishnah and the previous one is that here we are dealing with entire units, such as a cask of wine or an ox. If one of these which is forbidden such as a cask of wine that contains yen nesekh, becomes mixed in with a thousands casks containing kosher wine, they are all forbidden.
1) If one cask of yen nesekh is mixed up with even one thousand kosher casks, they are all forbidden.
2) If one statue used for idolatrous purposes is mixed up with even one thousand statues that were not used in idolatry, they are all forbidden.
3) In chapter two, mishnah two, we learned that idolaters would make circular holes and take out the animals heart and use it in worship. If a piece of one of these skins is mixed up with a large quantity of regular animal skins, they are all forbidden.
4) An ox that killed a man is to be sentenced to death (Ex. 21:28). If this ox becomes mixed up with other oxen, they are all forbidden. Note that in all of the cases of live animals in this mishnah, the same rule is true if the meat of the animal is mixed up with the meat of other animals.
5) This heifer is the one referred to in Deut. 21:4. It is used to expiate the blood guilty for a murder where the murderer has not been caught. If this heifer, after it has been designated to be part of the ritual and is on its way down to the wadi where its neck will be broken, should become mixed up with other heifers, they are all prohibited.
6) When a leper becomes cleansed of his disease, he must bring two birds as a sacrifice (Lev. 14:4). If they are mixed up with other birds, they are all forbidden.
7) When a nazirite ends his term of naziriteship, he must shave (Num. 6:18). Should his hair, once it is shaved off, become mixed up with other hair, it is all forbidden. In other words, no nazirite hair wigs!
8) The first born of a donkey is usually redeemed by giving a sheep to the priest in place of the donkey (Ex. 13:13). If this newborn donkey should become mixed up with other donkeys before it is redeemed, they are all forbidden.
9) If a piece of meat, cooked in milk should become mixed up with other kosher pieces of meat, they are all forbidden.
10) The scapegoat is the goat sent to Azazel on Yom Kippur (Lev. 16:22). If it should become mixed up with other goats, they are all forbidden.
11) It is forbidden to slaughter non-sanctified animals in the Temple court. If the carcass of an animal slaughtered in this fashion should become mixed up with other carcasses, they are all forbidden.

יין נסך – one jug in one-thousand jugs forbids benefit of all of them , but this is not the Halakha but rather, as we have written at the end [the chapter] "כל הצלמים" /all of the [idolatrous] images (Tractate Avodah Zarah, Chapter 3, Mishnah 9): They take the monies of that jug to the Dead Sea, and the rest – everything is permitted to derive benefit but prohibited to drink.

ועבודה זרה – a figure that was worshipped and mixed with one thousand figures which are not idolatrous.

ועורות לבובין – these are also forbidden to derive benefit from them as we mentioned in the chapter"אין מעמידין"/we don’t leave (Tractate Avodah Zarah, Chapter 2, Mishnah 3).

וצפורי מצורע וחולין שנשחטו בעזרה – things prohibited to derive benefit from and in Chapter two of [Tractate] Kiddushin (Mishnah 9) we explain them.

ושעיר נזיר – they are prohibited to derive benefit from as it is written (Numbers 6:18): “and take the locks of his consecrated hair and put them on the fire that is under the sacrifice of well-being.” And if a bundle of the hair of the Nazirite, een one thousand bundles of the rest of the hair, all are prohibited to derive benefit from them.

ופטר חמור – are prohibited to derive benefit all the while that it is not redeemed.

ובשר בחלב – a piece of meat that was cooked in milk and became combined with one-thousand pieces [of meat], it prohibits all of them regarding deriving benefit. And this Tanna/teacher holds that a thing where it is customary to be counted and its prohibition is one of deriving benefit, prohibits the mixture in any amount, and aall of these are considered in our Mishnah a thing where it is customary to be counted, and their prohibition is a prohibition of deriving benefit.

הרי אלו – o exclude that which is forbidden to derive benefit and it is not customary to count, or where it is their practice to be counted, and are not forbidden from deriving benefit, which do not forbid the mixture in any [even miniscule] amount.