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.
Plot hole: There's this remote drug hideout. A chopper flies by it, multiple salvos of uzis are fired, people are screaming...and yet this dude calmly approaches it and opens the door with a bag of groceries. Any of those sounds would have been heard for a mile or more in a place like that. There's no possible way that a drug merchant would unsuspectingly waltz into the place. And there's a buddy of his in a jeep (open one, too) waiting outside, who did not hear anything and nobody heard that vehicle approach, either. (00:39:20)
The Case of the Red-Faced Thespian - S4-E12
Plot hole: Magnum mentions that he spoke "one hour ago" to Robin, getting the description of Lowell Xavier Jameson. All the suspects are at the estate, and Tanaka arrived, apparently with an arrest warrant for Higgins, when Magnum still hadn't spoken with Robin. Magnum did have to bargain for Tanaka to put off the operations by two hours; it does not make sense that he'd be around at the estate one 1 full hour more for unexplained reasons.
The Case of the Red-Faced Thespian - S4-E12
Plot hole: Magnum is incredibly slow to unveil the charade at the base of the episode; he does it based on something marginal (Robin Masters does not do "research" for his novels), but he completely overlooks the key plot point of 1-17 "J. Digger Doyle" was that he does not use a typewriter, but he dictates the novels.
The Case of the Red-Faced Thespian - S4-E12
Plot hole: The plot of the episode has a big reveal that tricks the viewer making zero sense; the victim is alive and well, but there's an ambulance, they bring the victim away, and Magnum spends most of the episode in the noble effort of saving Higgins from a murder accusation. Magnum mentions "I figured I still had about a half an hour before Tanaka returned with a warrant for Higgins' arrest." even in his internal monologue, so it's not that he was trying to hide the fact from other characters.