Other mistake: Higgins hypnotizes Magnum using as pendulum a medallion, which is a reused prop from the very previous episode; Paulo, the "travelling companion" aka boytoy of his ex fiancée, was wearing it in the finale. It makes no sense for him to have it - unless you want to write your own dark fanfiction about it. It was just a throwaway prop, on screen for a second or two, and reutilized for another brief scene here. (00:31:50 - 00:47:25)
Revealing mistake: Chased by the bad guy who shoots over 9 times, Magnum makes a sharp, almost "U" turn; the car slows down during the turn, enough for the viewer to appreciate how thoroughly unlike John Hillerman his stunt double is, with his head full of hair. (00:33:10)
Continuity mistake: Higgins hobbles towards the club's beach bar in his horrid state (you'd think he wouldn't be caught dead looking so ridiculous) and starts reminiscing about the war and trying to mooch a cigarette. In the background, the same blonde with a black bikini hops over the wall twice, and same for the Asian with a blue/black swimsuit. Moreover, a girl in a red bikini and yellow towel keeps making back and forth walks by the surf on the beach. (00:29:30)
Continuity mistake: Rick tosses the lighter on the table when Magnum shows up tobacco-blocking poor Higgins. The lighter is in a spot on the table next to a paper cup that was never there and is gone after, and the lighter moves too. (00:30:45)
Continuity mistake: Randolph puts the secretary on hold as Weston Reese tells him his plan to keep Magnum a target. Randolph's arm is in a different position on the desk depending on the camera angle. (00:28:25)
Continuity mistake: Magnum is in James Randolph's office and 'the new guy' is talking to him. He says he disagrees on Magnum's hypothesis; in the transition both him and Randolph have very different positions, with Randolph's hand on the glass and arm raised differently, and J. Weston Reese's arms from crossed in front, to his pockets. (00:26:45)
Continuity mistake: Magnum is hunched over the Ferrari opening the door when the car first tries to run him over, but in close-up Tom Selleck is standing tall. (00:22:50)
Continuity mistake: In the very brief dinner when Claudia tells Rick that it's over between them, she casts a shadow behind her in close-ups, all the way to the left in the other shots. The difference in ambient lighting of the whole table spot is significant too. (00:18:20)
Continuity mistake: Magnum and the corporate executive are having a chat after the board meeting. Throughout the scene, the same extras (starting with a man in a blue shirt and camel shorts, a man with a brown pattern shirt, a woman with a baggy sand dress) walk back and forth over and over in the mall or behind them at the tables. (00:08:00)
Continuity mistake: When Magnum reports that he narrowed the possible spy candidates to those in marketing, his hands are crossed over - but in the next shot, he is crossing them again. (00:06:40)
Continuity mistake: Higgins' hand motion when he whips out of the cigarette case is incoherent between the various shots. (00:05:40)
Other mistake: A big deal is made of Magnum wearing a suit, both by Higgins and by Magnum himself when he speaks to others. You'd expect then this to be the first time we see him donning such a formal, wear and head into a corporate meeting, but he wore in fact a suit for a long portion of screentime just two episodes prior, in Ghost Writer (2-11).
Character mistake: Rick reveals Magnum that a certain person committed "security fraud." That'd be securitIES fraud. (00:40:20)
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.
Continuity mistake: At the end of the episode, Tanaka approaches Magnum on the hammock and they have a chat. Sticking out from Tanaka's pocket, first his pair of glasses, then a packet of cigarettes for most close-ups, then the glasses again. (00:46:20)
Continuity mistake: Dave drinks his glass almost reaching the end, but when Magnum pulls out of the gun, the glass at the edge of the table is half full. (00:43:00)
Continuity mistake: The husband of Magnum's client shakes hands with everybody; in the first shot his other hand is at his belt, it's in his pocket in the following. (00:08:40)
Other mistake: Magnum states his date of birth to the doctor; "August 8th, 1944." On his driver license in "Memories Are Forever" (when the General shows it to his wife) the date was January 5th 1946. (00:05:35 - 00:40:55)
Revealing mistake: When Magnum shoots the nun, the one who falls off is a stuntman who would pass off as Gargamel but not as Christopher Morley. (00:46:25)