We are commanded that all animal sacrifices be free of certain physical defects. It is forbidden to consecrate an animal that has defects (even temporary ones) or to cause a defect in a consecrated animal or to slaughter it or to sprinkle its blood or to burn its parts on the altar (even if it is a non-Jew's sacrifice), as it says "you shall not offer anything that has a blemish... it shall be perfect for acceptance, there shall be no blemish in it... you shall not offer these to Ha-Shem and you shall not make a burnt-offering of them on the altar... you shall not offer them to Ha-Shem... and you shall not offer your G-d's bread from any of these from the hand of a stranger"¹; and it says "You shall not sacrifice to Ha-Shem your G-d an ox or sheep that has a blemish".^2,a

If a permanent defect occurs in a consecrated animal we are commanded to redeem it provided it is fit to eat, as it says "[There you shall offer your sacrifices...] but according to the desire of your spirit you may slaughter and eat meat... [pure and impure together]".³ If a consecrated animal has a temporary defect or is unfit for sacrifice for other reasons it cannot be redeemed; nor can a non-animal sacrifice be redeemed if it becomes unfit or impure once it has been offered.^b

It is forbidden to offer as a sacrifice anything that has been used to pay for forbidden sexual relations or that was traded for a dog, as it says "You shall not bring the hire of a harlot or the price of a dog [to the house of Ha-Shem your G-d]".⁴ An animal that has killed a man or been used for idolatry or fornication is also unfit for the altar or for any sacred purpose, as it says "For their destruction is in them"⁵ -- anything that has been used for destructive purposes is unfit. We can offer animal sacrifices only if their species is certain and they were born naturally and only when they are at least eight days old (preferably, 30 days old), as it says "If an ox or sheep or goat is born it shall be under its mother for seven days, and from the eighth day onward it shall be acceptable [as a burnt-offering to Ha-Shem"].^6,c

It is forbidden to burn anything on the altar that was not commanded. Anything that is the result of sin should not be offered as a sacrifice; it is like a sacrifice that has become unfit. It is forbidden to offer leaven or honey on the altar for fragrance or together with any sacrifice, as it says "For you shall burn no leaven or honey as a burnt-offering to Ha-Shem... they shall not ascend the altar for a fragrant odor".⁷ We are commanded to salt everything that goes onto the altar (except for blood, wine, and wood) and we are forbidden not to do so, as it says "And you shall not eliminate the salt of your G-d's covenant from your flour-offering; you shall offer salt with all your sacrifices"⁸; but if this was not done the sacrifice is still fit unless it is a flour-offering.^d

All sacrificial things -- animals, wine, flour, oil, wood -- must be carefully selected and free of defects, as it says "They and their libations shall be perfect for you".⁹ One who wishes to gain merit should be liberal and should bring a sacrifice of the finest quality; indeed, anything done for the sake of G-d should be fitting and good, as it says "All fat shall be for Ha-Shem".^10,e

Sources:
1. Lev. 22:20-22,24-25	a. 1:1-2,4-7,10; 3:1
2. Deut. 17:1	b. 1:10; 2:6,10; 6:4-5
3. Deut. 12:14-15	c. 2:9; 3:4,6-8; 4:1,7-8,14; see Maaseh ha-Korbanos 1:12
4. Deut. 23:19	d. 5:1,3-5,9,11-12
5. Lev. 22:25	e. 6:1-2; 7:11
6. Lev. 22:27
7. Lev. 2:11-12
8. Lev. 2:13
9. Num. 28:31
10. Lev. 3:16