Gemara

(Beraisa): "Nivlaso" - (the meat of the carcass is Tamei,) but not the skin, bones, sinews, horns, or hooves.

(Rabah bar bar Chanah): Surely, these are not meat. The verse is needed only (to Metaher from Tum'as Neveilah even) if they were cooked and seasoned.

114a (Beraisa): One who cooks bones, sinews, horns or hooves in milk is exempt.

120a (Beraisa): "Ha'Teme'im (Sheratzim)" - the extra 'Hei' forbids their brine, Rotev and Kipah.

Rishonim

Rambam (Hilchos Ma'achalos Asuros 9:7): One who cooks skin, Gidim, bones, roots of horns, or soft hooves with milk is exempt. Likewise, one who eats them is exempt.

Magid Mishneh: A Beraisa exempts for the others, and surely the same applies to skin.

Poskim

Shulchan Aruch (YD 87:7): One who cooks skin, Gidim, bones, roots of horns, or soft hooves with milk is exempt. Likewise, one who eats them is exempt.

Beis Yosef (DH Kosav b'Shibolei): Shibolei ha'Leket (2:34) says that if the skin of the stomach is salted and hardened and filled with milk it is permitted. Since it hardened, it is like mere wood without any moisture of meat.

Shach (22): He is exempt, but it is forbidden.

Pri Megadim (Sifsei Da'as): In Chulin, it does not say 'soft.' Skin with milk is forbidden mid'Rabanan. The Rambam (Hilchos Ma'achalos Asuros 4:21) mentioned skins that are like the meat, e.g. of a fetus, under the tail, and the Ervah. Mid'Oraisa these are like meat; the same applies to meat and milk. Perhaps the Torah forbids eating or benefiting form them. Keneses ha'Gedolah (43) brings that once, merchants brought honey in (leather) pouches, and he forbade. Even though it is dry, it was wet for the time (24 hours) for Kevisah (pickling), unless the honey touched the side of the skin with the hair. When the flesh side faces the honey, we forbid, lest strands of meat were still attached to the skin. Even though pickling always forbids, skin itself does not have so much taste, so one may rely on the opinion that meat harms the taste of honey. We permit olive oil from pouches, for the pouch harms the oil.

Rema (10): If skin of the stomach was salted and dried and became like wood, and it was filled with milk, it is permitted. Since it dried, it is like mere wood without any moisture of meat.

Shach (33): The same applies to other innards. It seems that l'Chatchilah one should not do so.

Sifsei Da'as: The same applies to other innards, but meat as dry as wood forbids. Likewise, we forbid skin of the stomach through cooking, for it softens. We should be stringent also if it was soaked for 24 hours. We permit only if it was salted or was over the fire long enough (to totally dry out).

Pischei Teshuvah (21): A case occurred in which a man stuck his finger in an animal's eye for a cure, and it hardened and he could not remove it from his finger. He stuck it in boiling milk to soften it. Lechem ha'Panim permitted it, since it became as hard as wood. This is unlike the Sifsei Da'as, who is stringent about meat. Also, cooking softens it. The same applies to other innards, but meat as dry as woods forbids. Likewise, we forbid skin of the stomach through cooking, for it softens. We should also be stringent if it was soaked for 24 hours. We permit only if it was salted or was over the fire long enough (to totally dry out). Also Beis Lechem Yehudah (24) disagreed. However, Tif'eres Tzvi argues with the Sifsei Da'as, and is lenient even regarding meat, even if it was soaked for 24 hours. Also the Noda bi'Yehudah (YD 26) is lenient, but he says that this is only regarding meat and milk. Since the meat already dried, it has no more taste to forbid the milk, so it is not considered meat and milk. Forbidden meat remains forbidden after it dries out. Tif'eres Tzvi argues also with this. The Shach (114:21) says that we are not concerned for a strand of dry meat in saffron, just like dry skin of the stomach. This is unlike the Sifsei Da'as and Noda bi'Yehudah.

Tosfos (Chulin 112b DH She'ani): We require Drashos to forbid brine of Sheratzim and Tamei animals. There is no verse for Tamei fish, so its brine is permitted mid'Oraisa. How can Rabah learn from the verse of Tamei species to forbid brine of a Tereifah?!

Tosfos (Chulin 112b DH v'Rotvan): Why do we need a Drashah to forbid sauce and sediments (in a pot) of Sheratzim? Ta'am k'Ikar (if an Isur can be tasted in a mixture, the mixture is forbidden) applies to everything! The verse really teaches about their brine. The other matters are an Asmachta. Alternatively, it teaches about sauce and sediments, i.e. that dissolved Isur is like the Isur itself. One is liable for drinking melted Sheratzim it like for eating them, like we say about Chelev (120a). If so, how can the verse also forbid the brine? We can say that there is no reason to learn one of these more than the other, so we learn both. We cannot learn from brine to sauce and sediments, One might have thought that one is liable only for eating, e.g if the brine coagulated.

Chasam Sofer (YD 81): After skin of the stomach dries out, people soften it with water and whiskey, and extract moisture from the skin to be Ma'amid (curdle) cheese. We cannot permit based on the Shibolei ha'Leket, for perhaps it did not get hard enough. Also, here it is softened, so it is like meat. The Gemara said that Nochri cheese is forbidden because they curdle with stomachs of Neveilos. Tosfos asked that even stomachs of Kosher animals should forbid if they give taste! He answered that meat and milk without cooking is only mid'Rabanan, so we are lenient about a Safek (whether it gave taste). If the milk was not put in the skin of the stomach, rather, in a juice drawn from the stomach, there is another Heter. We apply Ta'am k'Ikar to liquids that come from Isurim through cooking, but not to what comes from suction or salting. Tosfos said that we do not need a verse for sauce and sediments through cooking, for Ta'am k'Ikar. It is needed for brine, which is not through cooking. If so, Ta'am k'Ikar does not forbid juice that comes from the stomach if the juice did not solidify. It is forbidden only like liquids that come from Isur. The Torah Isur of meat and milk does not apply to it. Nochri cheese was forbidden only because they curdle with stomachs of Neveilos. A verse forbids liquids that come from a Neveilah. This is if the skin of the stomach was softened only a little. If it was soaked for the Shi'ur of pickling (24 hours), this is like cooking, and real taste comes out. If they must soak it a long time, they should remove it before it is in for 24 streaight hours, and put it in again after an hour or so.

Igros Moshe (YD 2:23): Recently, they make gelatin from hide tanned for the sake of shoes and leather Kelim. Even skin that is like meat ceases to be a food after tanning (Chulin 122, Rambam (Hilchos Ma'achalos Asuros 4:21). Therefore, we should not forbid skins that are not like meat, even if they are from Neveilos, for their Isur (even before tanning) is only mid'Rabanan. The verse excludes skin from the Isur of Neveilah and Tamei species. To forbid them after tanning is a double (stringency) mid'Rabanan. We do not find that Chachamim forbade this. I did not even find an explicit Isur regarding (tanned) skins that are like the meat.

Igros Moshe (YD 2:27): If gelatin was made from skin of a Kosher animal and salted, is it considered Pareve? I lean to say that there is no Isur of skin with milk, even mid'Rabanan, even if the skin is moist. However, in practice one should be stringent, like the Pri Megadim. I permit if it is dry like wood, since the simple reading of the Rema permits. The Noda bi'Yehudah permits if it was soaked, and the same applies to cooking. We can permit, since even the Pri Megadim forbids only mid'Rabanan even if it is moist. Since it is dry, even regarding skin of the stomach, which pertains to an Isur mid'Oraisa it is a Safek how we rule, therefore, one may be lenient about (regular) skin. It seems that we may permit any Safek about skin. The questioner heard that gelatin does not give taste. One may not rely on this. However, since it seems that there is no Isur, and it is only a question whether one should be stringent like the Pri Megadim, perhaps one should arrange for people to taste gelatin of Heter to see if it gives taste. One may not consider something that can be verified to be a Safek.

Igros Moshe (DH v'Hinei): Darchei Teshuvah (87:5) says that skin is forbidden due to absorbed milk, but it does not forbid the milk, for it has no taste. If so, there is no taste of meat and milk in the skin. Why is it forbidden? Perhaps he means that skin itself has taste, but it does not give taste to what it is cooked with. If so, gelatin made from skin does not give taste to milk not absorbed in the gelatin, but milk absorbed in the gelatin will have taste of milk and of gelatin. If so, it is forbidden according to the Pri Megadim, who forbids skin with milk. However, if something does not give taste, there is no source to say that it itself has taste. Rather, it is a mere stringency to forbid meat cooked with skin, lest people cook meat and eat it with milk. We forbid the skin because (we are stringent to consider it like meat, and) there is taste of milk in it. We do not forbid the milk, for there is no taste of skin in it. Even if gelatin made from skin would have taste of skin, we cannot forbid it more than skin itself, and I explained that even the Pri Megadim holds that skin does not forbid milk. There is no room to decree, for the skin changed (to gelatin) and it is not at all evident that it came from skin.

Igros Moshe (DH Gam): Gelatin from skin is made from a juice that comes out of the skin only through a major process, but not through regular cooking. Therefore, we do not apply to Ta'am k'Ikar. It is like brine. A special Drashah forbids brine of Sheratzim and Tamei animals. There is no Drashah for Tamei fish, so their brine is permitted mid'Oraisa. If so, surely we cannot learn to forbid cooking brine of skin of Kosher animals with milk and eating it. Tosfos asked what is the source for brine of a Tereifah; the Ran says that the Drashah in Chulin 120a forbids it. The Chasam Sofer says that the Torah permits cooking milk with brine of meat. Even if mid'Rabanan one may not cook them together, this does not apply to brine of skin, even according to the Pri Megadim. All the more so we may permit gelatin with milk, even if it gives taste, for it is a mere stringency to be concerned for the Pri Megadim. However, gelatin from skin of Tamei species, Neveilos and Treifos is forbidden.

Teshuvas Minchas R. Aharon (R. Aharon Kutler - 17:22): We cannot permit because the gelatin by itself is improper to eat, since it is used to improve food, just like Se'or (sourdough. Even though it is improper to eat by itself, since it is used to ferment, one is liable for it on Pesach.)

Yevakesh Torah (2:12): There are five reasons to permit. 1) Most Poskim say that the Isur of bones and skin of Neveilos and Treifos is only mid'Rabanan. 2) If it changed to something else, this is Panim Chadashos. 3) All permit a taste that became Pagum and it is not intact. 4) Usually, there are 60 parts of Heter for each part of gelatin. Even if there is not, Mishnas R. Aharon says that since we never heard that anyone tasted gelatin in a mixture, there is a Shi'ur for Bitul. 5) All agree that one may rely on the Rashba who permits a Pagum taste that people use.

Note: Many disagree with many of these points, like brought above. Many Poskim forbid gelatin from bones and skin of Neveilos and Treifos letter of the law, and even those who disagree did not condone to be lenient in practice - PF, with thanks to R. Y. Spitz Shlita for helping me to clarify this Halachah.)

Yevakesh Torah (ibid.): However, many Gedolim distanced using bones and skin of Neveilos and Treifos. Shibolei ha'Leket (cited in Beis Yosef) said that in his locale, they were stringent not to put milk in skin of the stomach at all. Even ha'Ozer says in the name of Keneses ha'Gedolah that people do not eat cheese put in skin of the stomach even if it is as dry as wood; one should also forbid honey in skin pouches if it touches the side of the flesh. However, there perhaps we are concerned lest the skin of the stomach did not dry enough, and there is not 60 times as much as the skin. Also meat and milk is mid'Oraisa, but most say that bones and skin are only mid'Rabanan. Chazon Yechezkeil held that it is permitted, but he was concerned lest people say that Torah laws change based on Chachamim's will, especially since people thought that gelatin is made from marrow. Rashi (Yoma 40a) explains that we should not give opportunity for Tzedukim to say that Chachamim do everything they want. I do not know why they do not use bones and skin of Kosher animals. Regarding meat and milk, Mishnas R. Aharon (16:13), Igros Moshe and ha'Emek Teshuvah permit them.