Allowing Melachah which is not a Yom Tov necessity ["Mitoch"]
Do we permit Melachah which is not for a significant Yom Tov need, because it is already permitted for a significant Yom Tov need: Beitzah 12a-b
Engaging in initial sexual relations [which will likely result in bleeding] on Holidays: Ketuvot 7a
Lighting a fire to create a nice smell: Ketuvot 7a
Lighting a fire to destroy leaven for Pesach: Pesachim 5a-b Slaughtering a voluntary burnt offering [olat nedavah]: Beitzah 12a
Work for something which is of equal benefit for all people: Ketuvot 7a
Work for something which is universally considered a necessity: Ketuvot 7a
Work for the benefit of Temple Property [hekdesh]: Pesachim 47a
Work for the benefit of non-Jews: Pesachim 47a Liability for cooking and eating gid hanasheh [sciatic neurovascular bundle] in milk on Yom Tov: Beitzah 12a-b
"Shevut" [Rabbinic Prohibitions] on Holidays
Being more lenient regarding Shabbat than Yom Tov, because Yom Tov is inherently more lenient in its laws, leading people to possibly disregard its prohibitions: Beitzah 2a-b
Prohibiting movement of an item which has a permitted use on Holidays, if it is not a movable vessel on Shabbat: Shabbat 124a
Permitting Work with an Altered Form: Shabbat 117b, 128b, 148a, Pesachim 47b
Violation of a Rabbinic Prohibition for that Holiday, or for the following Shabbat, is permitted, but not fora "Distant" Use: Shabbat 114b, Pesachim 47a
Breaking one rabbinic prohibition to announce that another one is permitted: Shabbat 114b
Doing Work if one is certain that the first day was the real Holiday: Pesachim 52a
Taking care of a dead body: Shabbat 139a-b Separating a tithe and saying that it will take effect on whichever of the two days is not actually the holiday: Eruvin 39a, 39b; Beitzah 3a-b
Specific Forms of Work
Construction, Plowing and Completing Items
Building a temporary rooved structure, such as by adding shutters to a roadside stand: Shabbat 125b, 137b-138a; Eruvin 44a-b; Beitzah 10a, 11b-12a
Adding on to a temporary rooved structure, such as by removing shutters from a roadside stand: Shabbat 125b, 137b-138a; Eruvin 44a-b; Succah 27b-28a; Beitzah 10a, 11b-12a Covering blood after slaughtering: Pesachim 47b; Beitzah 2a, 7b-9a, 9b-10a Tithing dough: Beitzah 9a
Dancing [one might prepare an instrument]: Shabbat 148b
Making an item valid for use for a Mitzvah: Succah 33b
Above, where he didn't need that item at the time: Succah 33b
Plowing a furrow: Makkot 21b Burial: Beitzah 6a Digging a hole: Beitzah 7b-8b
Loans on Holidays, and their legality for claiming payment afterwards: Shabbat 148b
Taking collateral for a Holiday loan: Shabbat 148b Sanctifying a Celebratory Holiday Offering: Shabbat 148b
Sanctifying an Offering which is not brought on the Holiday: Shabbat 148b
Getting a portion of an animal Slaughtered on the Holiday, if he does/doesn't normally buy portions from the butcher's Slaughtering: Shabbat 148b
General Sanctification of animals: Shabbat 148b Dedicating an item to the Kohanim: Shabbat 148b
General Ex-Communication: Shabbat 148b Separating Terumah / Other Tithes: Shabbat 148b; Eruvin 39a; Beitzah 12b-13a Lottery of the Kohanim for [shares of] Offerings: Shabbat 148b
Conducting the lottery for yesterday's [weekday] Offerings, on Holidays: Shabbat 149b
Do the laws of transport and Eruv apply on Yom Tov: Beitzah 12a
Prohibiting transport of an unnecessary item on Yom Tov, because one may come to do it on Shabbat: Shabbat 124a-b; Beitzah 12a-12b
Transporting the challah dough-tithe or the gifts of meat or Terumah tithe to Kohanim on Yom Tov: Beitzah 12b
Acts which appear to be selection: Shabbat 134a
Selection in eating beans: Shabbat 142b; Beitzah 14b
Above case, differentiating between cases where there is more dross or more food: Shabbat 142b
Using a rag to cover a barrel of water: Shabbat 148a-b
Miscellaneous
Taking care of a dead body: Shabbat 139a-b
Aiding an animal in birthing: Shabbat 128b
Aiding a mother animal in becoming close to her child: Shabbat 128b
Clapping: Shabbat 148b
Striking one's chest: Shabbat 148b
Lighting a fire: Makkot 21b-22a
Using an egg that was laid on Yom Tov: Beitzah 2a-5b