A Succah for which an animal finishes the construction: Succah 8b; Menachot 42a
Requiring that the Succah be built via an act of construction ("Taaseh") and not by retroactive validation of prior construction, via a peripheral act of alteration: Succah 11b, 12a, 15a, 33a
Using stolen materials: Succah 9a
What if the Succah was constructed more than thirty days before the Holiday: Succah 9a