First off, I am not a lawyer, but my understanding of the US legal system is such that I believe Columbo is not breaking the double jeopardy standard in this case. A coroner's jury can only find the likely cause of death, it does not pass down a legal verdict (guilty/not guilty) or charges against a specific person. As such, Beth Chadwick has not been legally cleared of anything and is therefore still open to prosecution for the murder of her brother, Bryce.
This has never been one of my favorite episodes, either. I don't like Susan Clark or something. The hairstyling scene has always bothered me - it's so obviously NOT a real salon (see "Old Fashioned Murder" - the Daryl scene) it's a distraction. Also, the fashion sequence where Peter Hamilton can play pool and get a martini while his girlfriend buys a dress???? Were stores actually like that????
Also, the lightbulb throwing scene. Beth starts saying "Oh, stop telling me to calm down!" before Peter says "Beth, calm down." I could go on, but it's definitely not a favorite, despite the presence of Leslie Nielsen.