Other mistake: The episode opens with the Coast Guard finding the boat owned by Marion's father empty. It's a small sailboat. Later Magnum visits it with Marion, and the boat is a small double decker yacht that looks entirely different. (00:01:50 - 00:09:30)
Visible crew/equipment: When Magnum tips his hat to the group of Hawaiians who don't want any Haole messing with their channel, in his sunglasses there's the reflection of a set light and the crew. (00:08:40)
Continuity mistake: Marion Hammond unlocks the boat door and finds a mess. Between the establishing shot of the interior and the one with Tom Selleck inside, the towel on the ladder moved, and a diary tossed on top of the typewriter flipped without anyone coming anywhere near. (00:10:05)
Continuity mistake: On his way to Rick's boat, Magnum stops to talk with the witch lady. A very short drive and he's then in front of the boat. Rick is in the background and he starts moving and preparing to greet him, but in the close-up it's as if he has been chilling all along and only then decides to be active. (00:21:20)
Revealing mistake: When the masked Hawaiian hits Magnum in the back with the club, for a second you can see distinctly Tom Lupo (stunt double) 's face instead of Tom Selleck's. (00:22:25)
Continuity mistake: Magnum is saved, and it's time for the others to concern themselves with the assailant. Rick dives in a close-up to look for him. The mask is really close to him all of a sudden, and in a different position (practically touching Magnum's chest) in next shot. (00:23:20)
Revealing mistake: In the wider shot, the dead body the police covers has much more of a receding hairline than in the close-up. (00:23:55)
Continuity mistake: When Marion asks "He's dead, isn't he?" hair pops in front of her shoulder suddenly after the cut. In fact, throughout the whole scene notice how in close-ups it's in front of her shoulder, in wider ones behind her back. (00:24:25)
Continuity mistake: Higgins wants to show Magnum the rare Kudu buck in a book. Picking it up from the shelf, causes 3 other books to lean forward. In the close-up that follows, just one book is misplaced. (00:26:30)
Continuity mistake: Magnum puffs holding Keone's photo with his right hand - which was both hands before the sudden cut. He then drops the photo on the table, but when he digs the map from underneath the pad, the photo changes position entirely again during a sudden cut. (00:29:30)
Continuity mistake: After the culprit and Marion are aboard safely, there's a shot of Magnum with the bomb in close-up, followed by another one where the timer went back almost at the starting point. (00:44:40)
Continuity mistake: To nobody's surprise, Magnum emerges from the ocean unscathed. Between shots, his hand and Rick and the villain's change positions. (00:45:15)
Continuity mistake: Marion and Magnum walk to the taxi for the goodbye. He opens the door, and her hair is all behind her back. Switching to the frontal view, she has her ponytail in front of the left shoulder. (00:46:00)
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.
The Woman on the Beach - S2-E3
Continuity mistake: The woman in white leans over the back of a chair and clears her throat to discreetly shoo away an officer with his belle. There's difference in lighting between close-ups and the rest, and the position of the loose end of her scarf changes as well. (00:02:45)
The Woman on the Beach - S2-E3
Other mistake: First scene set in present day. Exterior shot of Rick's club. A sign says "King Kamehameha Club - Est.1905", In the previous season, episode 11 was focused on the club itself, and Magnum met the landlord, Mr. Sidney Dollinger, who explicitly said "I founded that club for the people.", and Magnum, regretting accusing him, mentions that he blamed "an 80-years-old man." Even assuming he was not precisely 80 in 1981, in 1905 he still would have been a pre-teen or barely a teenager, not the rich planter who founded Hawaii's most exclusive club donating a vast domain to it. (00:05:30)
The Woman on the Beach - S2-E3
Continuity mistake: Rick asks Kemo the bartender for a cigarette. In the background, a man in black walks by a tiki torch. Cut to Kemo for a second as he hands him the cig, and when Rick is back in frame, the man in black is walking by another tiki torch that was several meters earlier in his path. (00:09:00)
The Woman on the Beach - S2-E3
Continuity mistake: The Woman on the Beach is actually on the beach and talks to Rick. She says; "I wish I could be that way" across two shots where the position of her scarf changes completely. (00:11:55)
The Woman on the Beach - S2-E3
Continuity mistake: Sara puts a hand on Rick's shoulder as he goes to get more wine. Her face now has more hair strands loose down her cheek and temple. (00:12:40)
The Woman on the Beach - S2-E3
Continuity mistake: Magnum and Rick's relative distances seem to be quite off when they are talking to each other from the respective cars; the Ferrari's driver seat seems to be past Rick's in Tom Selleck's close-ups, but when Larry Manetti is talking, he's looking at Selleck's stand-in (sit-in, rather) from a noticeable distance ahead. (00:14:50)