If an item is still in a preparatory state, but is already useful: Shabbat 141b
If an item is connected to the ground: Shabbat 81a
Purification
Whether implements require physical alteration, and not a mental change of use, to remove impurity: Succah 13b-14a
The minimum size of a hole in a non-business vessel to remove the vessel from Impurity capability is that of a Pomegranate: Shabbat 112b; Eruvin 4b, 24a; Succah 5b-6a
If a hole was smaller than a Pomegranate, and then was fixed, and then another hole was made which would have combined with it to reach a Pomegranate: Shabbat 112b; Eruvin 24a
An implement losing Impurity if it is digested, while whole, by an animal: Menachot 69a
Purifying a "tanur shel achnai" - an oven comprised of joined segments: Berachot 19a; Bava Metzia 59a-b
Purifying an oven requires breaking it into parts that are not the majority of the original oven; what if one splits the oven in precise halves?: Bechorot 17b
Implements made of specific materials
If a wood Vessel is not mobile when empty or full: Shabbat 83b; Megillah 26b
If a wood Vessel is flat, without projections: Shabbat 123b
For pottery implements, there is no concern of mobility: Shabbat 83b
Size of a clay pot's hole to render the plant inside the pot "connected to the ground" beneath [depends on the pot's usage]: Shabbat 95b-96a
implements made of Feces, Stone or Earth do not receive Impurity: Shabbat 96a, Menachot 69b [and for an example of such an implement, see the Maroka on Bava Metzia 47a-b
Whether an implement constructed during digestion by an animal is considered an implement made of feces or not: Menachot 69a-b
A cloth of less than 3 square finger-breadths: Eruvin 29b-30a; Succah 16a
Considering something a garment based on popular use: Eruvin 29b-30a
A sponge: Shabbat 143a
A bed: Succah 16a
A glass vessel which was pierced, and then sealed with lead: Rosh HaShanah 19a-b
Items which are inside clay pottery along with an impure item, where the impure item is in its own sealed segment: Niddah 17a-b
An implement with a sheretz inside it doesn't make implements Impure inside it: Shabbat 138b, Pesachim 20a-b
The status of an item on which a formerly impure utensil is found, when it is unclear whether the utensil or the item was capable of communicating or contracting impurity at the moment of their initial contact: Niddah 4a
Making liquids or foods impure, where the vessel received impurity from a liquid: Niddah 7b
Implements which have differentiated insides and outsides
If impure Liquids touch the outside, or the inside: Pesachim 17b; Niddah 7b
If a sheretz touches the outside, or the inside: Pesachim 17b
The difference between implements which become impure from their insides/outsides: Niddah 7b