血: xuè , xiě, what's the difference? Is there some sort of logical rule for when 血 is xuè and when it is xiě?
The standard Chinese dictionary (《现代汉语词典》) lists xuè (fourth, not third, tone) as the official pronunciation and xiě as a colloquial variant. As such, in most compounds and technical terms, xuè is preferred. The pronunciation xiě is acceptable when you just want to say "blood" in casual speech.

There are several exceptions: the two modifiers 血糊糊 (xiěhūhū, "covered in blood") and 血淋淋 (xiělínlín, "gushing blood") are never read with the xuè pronunciation. There is also a word "血晕" the meaning of which differs based on which pronunciation of 血 is used.

血晕 (xiěyùn): to bruise
血晕 (xuèyùn): a traditional Chinese medicine term for fainting after childbirth due to loss of blood.

Note that this is only what the dictionary says. I suspect many native speakers make different choices in their own speech.