Other mistake: With power out Magnum somehow lights the gas stove with the knob, which is electric. Should have used a match. (00:26:40)
Character mistake: The party is supposed to be "One of the premiere social events of the season", but the only people invited (Higgins knows for sure who is gonna come, so it's not like there's low attendance because of the weather) are a Prince from a fictional European state nobody knows about with his commoner wife, the editor of a poetry magazine that needs Robin's funds to survive, a sports star and Robin's accountant. 5 people in total, already all in Robin's pocket, and nobody else in attendance. While you could say that having royalty and a golden glove winner is certainly noteworthy, those people don't meet anyone else. Hardly a 'social event'. (00:04:00)
Visible crew/equipment: When Rick and TC are boarding up the dining room window, the actor's white tape mark is visible in the floor, between their feet. (00:36:30)
Visible crew/equipment: When Magnum and Higgins go to the kitchen to boil water, for a spot of tea, a white tape mark is visible in the floor, near the sink. (00:26:15)
Other mistake: The killer is finally in action; they get a semiautomatic with a silencer from a case, then they do an ominous gun-in-hand walk bit (filmic stereotype where someone just walks with a gun out for no reason instead of concealing it). The shadow of the gun there though shows no sign of a silencer. The killer shoots indeed with a silencer - the audio implies that - but in the shadow you can see it is now a revolver. (00:44:20)
Factual error: This episode is set during a party happening on the weekend of Spring equinox, which means end of March. but it's also happening during a devastating hurricane. No hurricane (not tropical storm) has ever occurred in Hawaii in that month or anytime close to that; hurricane season in the Pacific starts at its earliest in May, and used to begin towards July in the 1980s climate.
Continuity mistake: When Wanda Martine, Princess of Turbia has a giggling fit at the expense of Candice Wingate's dead husband, she holds no glass, but was holding one in the previous shot. (00:24:40)
Revealing mistake: The criminals have to get back inside the house because the cars for their getaway are "waist deep in mud", but they show no sign of having been anywhere near them; their shoes and bell bottom jeans are spotless. (00:22:35)
Continuity mistake: When Prince Roland calls the bandit "Impressive, but foolish", his wife's hand is on the table holding a cocktail umbrella all of a sudden at the cut. Later in the same scene her other hand holding a glass peeks in view showing she is drinking, but in an intermediate shot she is actually pouring the drink in another glass, moving the hand in another direction. (00:23:20)
Continuity mistake: The wine stain on Higgins' chest changes shape and size throughout the episode; in particular you can notice from the wine cellar to the sequence upstairs when Magnum spills the drink the stain gets longer and thicker on the button line. (00:18:30 - 00:19:10)
Visible crew/equipment: When Higgins whispers to the dogs to 'Stay' after the ruthless home invader shot a hole in the barrel, in the close-up of the dogs you can see in the background a crew member in the upper right corner, by the broken barrel. (00:18:00)
Continuity mistake: The criminal at first has his shirt wet in the shoulders area and down his collar and buttoned center. In the wine cellar scene, the center is dry, and returns wet when they return in the dining room after shooting Higgins' radio (and Robin's immature wine). (00:16:00)
Character mistake: Higgins is narrating one of his stories, this time implying that he helped Hemingway write "The Old Man and The Sea." Normally Higgins' stories are somewhat plausible because of factual accuracy that leaves room to be taken at face value, but here he says that it happened in "The Florida Keys, '53 or '54, it was." while "the manuscript was only in the outline stage." The novel was published in 1952. (00:10:30)
Continuity mistake: Magnum in his fangirly reaction to the Tigers' ace player is barely able to point him towards the dining room. In the shot from behind he at least brings the umbrella back in its original position, but it's still across his chest and in front of the opposite shoulder in the front view. (00:10:00)
Continuity mistake: Duke Davis hands Magnum his umbrella, hook of the handle facing his left. It faces his right in the close-up of an ecstatic Magnum. (00:09:25)
Other mistake: The accountant first, then some minutes later the prince and princess arrive at the estate. They are bone dry despite the hurricane outside complete with pouring rain noises and strong winds. (00:05:35)
Other mistake: The Prince and Princess of Turbia are, according to Higgins, "Fixtures at Robin Masters' parties." Makes no sense then that they have no idea how Higgins looks like, since it's established that he's been taking care of the estate for over a decade - of course, Masters does not reside in Hawaii himself a lot, but earlier in the episode it is established that he runs those parties at his villa yearly.
Character mistake: Higgins addresses constantly the Prince and Princess of Turbia as "Your Majesty." For an expert of protocol as Higgins, it's quite odd to make such a mistake; "Your Majesty" is used for royalty with a rank higher than Prince (kings, emperors). Paradoxically, Magnum gets it right, calling both "Your Highness." (00:06:30)