What are the flaws that invalidate Ud-hiyah (sacrificial animal offered by non-pilgrims)
and those which make it reprehensible but valid? What is the best type of Ud-hiyah?
The invalidating flaws in Ud-hiyah and Hady (sacrificial animal offered by pilgrims) are being one-eyed, blind, obviously sick, too thin, lame, or having broken horns and ears. The best type to sacrifice is camels, then cows, and then sheep. It is also better to sacrifice the fatter and the better looking ones. As for the details of the desirable and the reprehensible, you can refer to the books of Hadith and Fiqh (Islamic jurisprudence) in this topic for more information.