Plot hole: When Jessica is arrested for the murder of the enemy agent. Her purse is confiscated. It was reported stolen by Michael Haggerty. But throughout the whole show none of the cops looked at her ID. Besides that she's a famous women and someone at the police station would definitely know who she is.
Murder, She Wrote (1984)
1 plot hole in season 5 - chronological order
Audio problem: When singing "Goodbye little yellow bird" Emma blows a kiss to Oliver offstage, but she is still singing the song when she is blowing the kiss. Although it's possible she was pretending as it was part of the act, her voice wasn't even muffled by her hand.
Trivia: The song Angela Lansbury sings, "Little Yellow Bird," when she plays musical hall performer Emma, is the same song she sang in the 1945 film The Picture of Dorian Gray, when she played music hall performer Sybil Vane.
Question: Why did Lane Henderson (Louise's father) murder his wife?
Answer: In a flashback scene, it was shown that he had a violent temper, so it stands to reason that he finally killed her in a fit of rage.