Plot hole: Magnum is defending his client from the detective's interview, and doing so he says "The bomb that blew up Lindsey's car could've been planted at any time yesterday." Now, Magnum had no way to know that the murder happened through a car bomb; he just learned of Bart Lindsey's death from Higgins, and he rushed to the beach without getting additional info, nor seemingly this info was given by the police crew in the first place. but he knows! Magnum is obviously the murderer. Not really, but it's the kind of statement that gives a murderer away in traditional whodunits, generally. (00:31:00)
The Elmo Ziller Story - S2-E20
Plot hole: Considering the reveal about 2/3 into the episode, Higgins appearing to Magnum coming down the stairs of the estate at the beginning does not make sense. Spoiler; it is revealed that he was Elmo all along, but then he would have had - with his terrible athletic ability as shown in previous episodes - to run across the estate beating Magnum to the villa or somehow find a way to the top floor that is never shown throughout the whole series, change clothes and - with the lads! - come down without breaking a sweat.
Plot hole: Taylor has the case scouted in such a way that you'd wonder what did he even need Magnum for in the first place; somehow he knows that the bad guy is in Hawaii (which is where the widow happens to live too), he knows he is seeing some girl and who she is, and got a picture of her too. If Magnum did what he asked, he would have arranged a meeting with her away from the gorillas - he does not insist to accompany him or anything of the sort, and in fact he needed only TC for that. Also, somehow Taylor knows as well where the bad guy's hideout is, but Magnum never returned with that information.
Plot hole: Taylor sets a timer on the claymore mine to make it explode within 10 minutes instead of by passage or by remote control, which is already pretty inefficient considering he went through the trouble of altering the original design, but even with that considered, it's inexplicable how Taylor knew that his target would be at that particular gazebo of the large estate, precisely at that time, within 10 minutes. To even get there he needed to ask TC, surely he's not privy to the victim's every habit nor schedule.
Plot hole: With the murder happening literally on tape, it's quite extraordinary and inexplicable that the police did not acquire the footage as evidence, especially with film buff Lieutenant Tanaka investigating, who is not fooled by the culprit's act. The footage would have been used for insurance reasons as well, and instead it is reduced to some novelty everyone checks out just to fight boredom on an evening at the estate.
Italian Ice - S2-E15
Plot hole: Magnum leaves the estate on the Ferrari leaving Katrina behind. He joins Margo at the drama lesson. Somehow, Katrina manages to be there at the same time as he is - without really knowing where he is in fact going, and it is her first day in Hawaii - and scratches his car in a temper tantrum.
Plot hole: Magnum gets through a wild goose chase because of two false clues, but their presence is not explained in the denouement nor makes sense. Magnum suffered no real amnesia, he says, and it's proven Magnum has never been to either places, so the parking ticket and card must come from the killer, linking them to the murder in an unnecessary way. They fill screen time nicely but do not fit the murder scheme.
Plot hole: The key plot point needs that the mechanics fixed a car completely wrecked in large parts of the chassis. So nobody gave it as much of a test run after working extensively on the aerodynamics, nobody sat on it for a moment, nobody drove it a few meters from the tow truck to the work area, at all and a single mechanic of the large car shop is able to say that with absolute certainty. It's an enormous stretch - not to mention that while Selleck's slouched posture in the episode makes it not entirely unbelievable, he is taller than Mark Withers by an inch, and the Ferrari was modified in real life to accommodate Selleck's size - there would be no way to push the seat further back, and the plot point is unnecessary for the resolution.
Wave Goodbye - S2-E7
Plot hole: For two patrol officers (one of them being kinda green) in Honolulu, Kelly and Jordan sure seem to have the weight of the entire State on their shoulders; they also investigate extensively the murder case, and they, until a month before, "worked drugs in that area", which was a piece of jungle around Maui. It's like the department for this episode and this episode only has no detectives, and a couple of random beat cops are covering the archipelago with highly specialized duties.
Plot hole: Magnum and Rick manage to switch Yuri with Fillipovitch through sheer magic; they base their infiltration on a little boat barely big enough to contain the two of them, with no room for them to hide the uncooperative Russian, plus we see most of their movements including them climbing up. It's simply a 'shocking reveal', but it's not setup in any believable way.
The Woman on the Beach - S2-E3
Plot hole: The episode has a small bit of supernatural hints, but the foundation of it is rooted in reality and acted by a living and not magical person. With that in mind, confirmed moments when the 'ghost' is Lisa in the flesh make no sense at all; her disappearance at the beginning is a Batman-like feat she shouldn't be able to execute. Not to mention that she is at the right place and time when Magnum visits the old abandoned estate; unless she just camps there 24/7, she had no way to know when Magnum (who visits 2 days after, not even right after the fact) would investigate.
Plot hole: Magnum asks Mac to "put together a list of ships that went down in that channel in the last 200 years." He gets the list, and it turns out of the ship of interest, amongst the many, is the Eldora, "a Spanish galleon used to carry the plunder back from Spain's numerous conquests." That sounds like something quite more ancient than 200 years, however it can be said that galleons were still in use in the early XVIII century. However, when Professor Martinez hears the news, she says that it supports her theory of early contacts between native Hawaiians and Conquistadores, which would put it centuries off range again. It also begs the question; why would the US Navy intelligence know of that galleon (but without any location or additional info) but the scholar at the university who is studying and publishing a book on that very subject is totally oblivious about it? Even Higgins heard about it.
Plot hole: The plot of the episode is nonsense. The boss of the company knows that Magnum made no progress and is on the wrong track, since he suspects someone in Marketing - it should also be noted that Magnum is mystified knowing that the President has the access codes, but he himself has them, and it would be a given to learn who has the various codes as first thing in a security analysis like he conducted. Yet for a couple weeks this Prez guy sends his wife to just sleep with the PI's friend, for...no discernible reason, other than create a diversion he did not need and that hinges on events and reactions that non only he couldn't predict, but also have nothing to do with facilitating his espionage, considering also that a more competent security firm is hired right after. Likewise, why would the guy from R&D try to "scare Magnum off" doing an attempted murder that is sure to get him arrested when he knows Magnum is focusing on the wrong department?