Forty Years from Sand Island - S3-E17
Plot hole: The culprit is in cahoots with the man that Magnum is trying to expose as WWII war criminal, and fears nothing from him, as he even explains to Magnum later; in fact he is his goose with the golden eggs. Yet he, a politician, kills his guy in broad daylight, for no reason, running the risk not only to be caught red-handed, but also more logically to be linked to him due to the investigations that will unveil the deceased as one of his major supporters. Instead, he does not touch Magnum, someone he has no connections with and tons of potential enemies. Let's not forget that the main motive that pushes Magnum to investigate is his assumption that someone wanted to kill Higgins, which is not the case, and the culprit knows that.
Plot hole: Magnum is amazingly naive in this episode, blindly believing the story about Tracy Spencer being a cop against every possible evidence of the contrary. This buffoonery aside, Tracy saves him from the two girls identifying herself as a cop, but a couple scenes later they both go meet their boss and try to set up a sting passing off as dealers of stolen goods. That does not make any sense.