Whether an action is necessary in order to consider an item a "vessel": Shabbat 125b-126b
Whether Items Prepared for Animals are considered Prepared for People as well or not: Shabbat 121b, Pesachim 56b
Whether Items Prepared for People are considered Prepared for Animals as well or not: Pesachim 56b
Whether the item must be prepared for the owner, or for people in general [such as Terumah]: Shabbat 127b
Items which are not usable when the sun sets, beginning that day: Succah 46b
Items which are locked inside a cabinet, in which a gap develops on Shabbat: Eruvin 34b-35a
Items which are expected to "Arrive" on Shabbat, such as river-water or feces: Shabbat 121b
Considering items in storage to be "unprepared" for use: Shabbat 126b-127a
An item which is not a vessel, but has a use [like a rod for clothing]: Shabbat 140a-b
A rope from which edible food is dangling: Shabbat 140b
Designating a set of items from which you will select one on Yom Tov, and then retroactively identifying the specific one on Yom Tov itself: Beitzah 10a-b
What happens if one designates items, and then isn't sure on Yom Tov whether the item before him is the same one he designated: Beitzah 10b-11a
Issues of the Use for which an Item is Designated
Using an item for a use other than its main use: Shabbat 123a; Beitzah 8a [hot ashes, garden soil]
Moving an item for a use other than its main use: Shabbat 146a; Beitzah 10a, 11a [chopping block]
Use of a vessel for a permitted use, when it also has a forbidden use [Undoing a Clothes-Press]: Shabbat 141a
Use of a vessel for which the parts were separate before Shabbat: Shabbat 122b
Issues of Designating Item for Use, to Move it
Moving a Vessel to use with/for something which may not be moved on Shabbat: Shabbat 107a, 121a-b, 128b
Moving an item which has no use on Shabbat, for use of its location: Shabbat 126b
Beginning the emptying of a storehouse on Shabbat: Shabbat 126b-127a
Moving the storehouse items with one's foot, while walking: Shabbat 127a
Designating a bird before Yom Tov for slaughter on Yom Tov: Beitzah 9b-10a; 10a-11a
Designating Broken Vessels and Vessel Lids for use
Showing intent by throwing a vessel into the trash before Shabbat: Shabbat 124b-125a
Dirt, or ashes from an oven: Beitzah 2a, 8a
Broken vessels, which are fit for a form of their original work: Shabbat 124b-125a
Broken vessels, which are fit for any work: Shabbat 124b-125a
Above two cases, differentiating between whether they broke on Shabbat or before Shabbat: Shabbat 124b
Moving a lid, in general: Shabbat 126b
Moving a lid, where it is used in connection with the ground: Shabbat 126b
Moving a lid, where it is used for a vessel which is connected to the ground: Shabbat 126b
Moving a lid, where the lid is a vessel unto itself: Shabbat 126a-b
Moving a lid, where it has a handle: Shabbat 126a-b