Here's a good one:
Mainichi translates this as: "Tokyo metropolitan gov't appeals ruling of police negligence in murder case." A few points struck me as interesting:
(1) It was apparently a murder in which the woman had been confined:
監禁 【かんきん】 (n,vs) confinement + 殺人 【さつじん】 (n) murder
(2) The negligence specifically relates to the course of the investigation:
捜査 【そうさ】 (n,vs) search (esp. in criminal investigations); investigation + 怠慢 【たいまん】 (adj-na,n) negligence; procrastination; carelessness
(First paragraph: "The Tokyo Metropolitan Government has filed an appeal against a court ruling that ordered it to pay 20 million yen to the bereaved parents of a murdered woman on the grounds that police were negligent in investigating the case.")
On a side note, "deriliction of duty" is 職務怠慢 【しょくむたいまん】.
(3) The Japanese headline uses the word 訴訟 【そしょう】 (n,vs) "litigation; lawsuit" to modify the term "investigatory negligence," rather than the word for decision:
判決 【はんけつ】 (n,vs) judicial decision; judgement; judgment; sentence; decree.
I find this a bit odd; I wonder whether 訴訟 can be used more broadly to indicate the court's ruling, outcome of litigation, etc. Can anyone clarify?
(4) It's a "koso," or initial appeal to a higher court, 控訴 【こうそ】, rather than a 上訴 【じょうそ】 (n,vs) , final appeal. Very handy distinction.