Plot hole: At the end of the episode McCoy and his team tape a conversation between Melissa Corbin and her mother Lorraine in order to record her admitting to murdering Alan, her first husband. Trouble is, she says nothing incriminating. The closest they get is Lorraine asking her why she killed Alan, and she replies "You didn't have to sleep with him." That means nothing, and in fact Lorraine says absolutely nothing of any legal significance during the entire conversation.
Law & Order (1990)
1 plot hole in season 12 - chronological order
Executioner - S18-E9
Factual error: Yost attacks and kills an innocent man, believing him to be Dr. Horace Garrison, a physician who administered a faulty lethal injection to a condemned prisoner, reducing him to a vegetative state rather than killing him. The problem is, medical doctors never, ever participate in an execution except to certify death, a legal requirement. They do not, ever, take an active role in killing the condemned person.
Det. Lennie Briscoe: Even though you are a taxpayer, you know, we don't actually work for you personally.
Trivia: Both Jerry Orbach (Det. Lennie Briscoe) and S. Epatha Merkerson (Lt. Van Buren) played guest roles before joining the cast. Orbach played a lawyer in the episode "The Wages of Love" in season two, and Merkerson played the mother of a victim in "Mushrooms" in the first season.
Question: Why did Arthur fire Serena?
Answer: He believed that she had become too empathetic towards the defendant they had been prosecuting, and that her actions were driven by her emotions instead of facts. While empathy is a good quality in general, a certain degree of detachment is required in order for a prosecutor to do one's job effectively.
Suggested correction: I'm not sure where you're getting your information, but medical doctors are involved in lethal injections more than just certifying death. This is why so many groups were actively trying to stop the practice of medical profession involvement. In 2007, 17 states required physician involvement, which included doctors at times having to administer the injection.
Bishop73
The botched execution took place in South Carolina, which absolutely forbids medical practitioners to take an active role in killing a condemned prisoner. In fact, they are considering switching executing prisoners by firing squad instead of lethal injection, at least partly to distance medical professionals from the actual procedure leading to a person's death.