[The following is posted from: The Conditions of a Sacrificial Offering – Imaam Muhammad bin Saalih Al-‘Uthaimeen ]
The Third Condition: The animal must be free of any defect that would prevent its slaughter from being valid and acceptable. These defects are of four types:
1. Clear defectiveness of the eye: This is when the animal’s eye becomes sunken or it sticks out to the point that it looks like a knob or it becomes a pale white indicating clearly that it is one-eyed.
2. Clear illness: This is when the animal exhibits signs of sickness, such as a fever that keeps it from grazing and causes a loss of appetite, or an obvious scabies infection that will spoil its meat and harm a person’s health (if he eats it), or a deep wound that threatens to affect its health and so on.
3. Clear limping: This is when the animal is unable to step safely (without hurting itself) when walking.
4. Emaciation that causes brain loss: This is based on what the Prophet said when he was asked about what types of animals one should avoid when sacrificing.
He gestured with his hand and said: “They are four: The lame animal that clearly walks crookedly; the one-eyed animal that clearly has a defect in the eye; the sick animal that clearly has signs of illness; and the emaciated animal that is (usually) not picked.” 
This hadeeth was reported by Maalik in al-Muwatta from Al-Baraa’ bin ‘Aazib. In another version of this report narrated by Al-Baraa’ found in the Sunan collections, he said: “The Messenger of Allaah stood up amongst us and said: ‘Four types (of animals) are not permissible to use as sacrificial offerings…’ and he went on to mention them.” 
So therefore if these four defects are found in an animal, they prevent its slaughter and sacrifice from being valid. This goes as well for any other defect that is similar to or worse than these, which means that it is also not valid to sacrifice the following types of animals:
1. A blind animal that cannot see with both its eyes.
2. An animal suffering from nausea until it releases its load and its harm is removed.
3. An animal that has been assisted in giving birth if natural delivery is difficult until the threat of danger is removed.
4. An animal afflicted by something fatal such as choking, falling from a high place, and so on until the threat of danger is removed.
5. A crippled animal, which is an animal that cannot walk due to a physical disability.
6. An animal with one of its front legs or back legs broken.
So if these last defects are added to the four mentioned in the narrations, the types of animals that cannot be slaughtered become ten in total. There are these six types plus the animals that suffer from the four previously mentioned defects.
 Al-Muwatta: Book of Sacrificial Offerings (1)
 Sunan Abee Dawood: Book of Sacrificial Offerings (2802); Sunan at-Tirmidhee: Book of Sacrificial Offerings (1497); Sunan an-Nasaa’ee: Book of Sacrificial Offerings (4369); Sunan Ibn Maajah: Book of Sacrificial Offerings (3144); and Musnad Ahmad(4/300)