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)
Revealing mistake: The killer nun is making "his" escape; shoots dead one secret service guy who in the spirit of 80s network television shows not a drop of blood and is propelled through the air as if he was hit by a cannonball and not some little silenced pistol. (00:45:25)
Other mistake: The priest and altar boys have the slowest reflexes ever; they stand as if nothing happened during the whole shootout, and can be seen finally covering behind the altar only after a few cuts, after the shots have already stopped. (00:45:05)
Continuity mistake: Magnum and Kate have the "I am mad at you" "And I'm mad at you!" exchange. When the camera angle changes, the sheets in front of Magnum slid past the edge of the table a bit. (00:36:55)
Audio problem: Kate answers the phone at the club saying "Hello?" without moving her mouth. (00:31:35)
Other mistake: The bicycle the killer uses is recognizable for its unique color pattern as the same prop used in the season 1 finale, when it was supposedly an expensive gift from Robin Masters, imported exclusively from Italy. (00:31:15)
Continuity mistake: Inside Rick's room with both him and Mac waiting, Magnum pours his drink from the decanter in his right hand, and then left hand. (00:28:55)
Continuity mistake: Magnum drops by at the hotel where he expect to find Kate and the Jororo delegation. As he pulls over in front of it, there are two elder ladies walking by, away from the hotel. One of them is wearing bright yellow pants and a very colourful top with horizontal stripes. Magnum gets into the hotel, and one of the extras he walks past right as he approaches the concierge, is that lady. And the other lady she was walking with, in a blue dress with white and red palms, is at the same desk. (00:21:45)
Continuity mistake: Kate Sullivan is interviewing the Prime Minister. Notice the position of the cane next to the end of the armrest at the beginning, and then when she is called to the phone; the cane is now at a different angle on the opposite end. (00:20:00)
Revealing mistake: Higgins is explaining the story of Bannister, which he conveniently happens to know all about. In Magnum's reaction shot, you can see that he starts giggling a moment before Higgins actually gets to the amusing part (that he was specialist at posing as a female). (00:17:50)
Continuity mistake: Magnum buys wine from Higgins using his potpourri of crumpled cash. He then walks past him dropping the casual line about MI6: from one shot to the next, his left hand moves from the neck of the bottle to the belly. (00:16:55)
Continuity mistake: In the scene with Mac and Rick fishing at the marina, continuity is all over the place as far as their hand movements is concerned; they move the fishing line with one hand that becomes the other in the next shot, several times. (00:13:00)
Continuity mistake: Magnum checks out of the photo Kate Sullivan gave him. First shot and close-up, he's looking at it holding it between his fingers, placed on the side. Next, he's holding it in one hand by the bottom. (00:10:50)