Revealing mistake: When the bad guys show up at the main door surprising Higgins, the background (save a couple plants at the side of the door) is matte painting. (00:42:50)
Continuity mistake: During the episode, Magnum is missing the scar on his chest and the one on the top of his shoulder. At least the latter, carried consistently from the pilot episode, is well visible in the following.
Revealing mistake: Magnum finds inside of the mysterious woman's villa a folder about Higgins. On the right side, there is some insurance document stuff that is pure filler. On the left side (but that one fades fast so you may need to pause for that) you can see that truly she has him scouted thoroughly, because it contains information about not just Higgins, but...John Hillerman and his acting career. (00:30:10)
Other mistake: At the appointment / trap at the abandoned shrine, Magnum hears a bell toll. He turn around, and it's clear that someone rang the bell pushing the log - it is still moving, it's not an automated system and there's no wind. but since the plot does not involve it, he just goes on like nothing happened. For all he knew, it could have been exactly where his supposed client or informant wanted him to go. (00:18:00)
Character mistake: Sitting at the club's beach bar, when TC urges him to give him the rest of the money Rick says "eighty" when he is in fact giving at least the 9th 10 dollars bill. (00:16:20)
Continuity mistake: When Jennifer tells off Magnum asking "You don't give up, do you?" Tom Selleck's wet hair is all frizzled up in different curls on the forehead between the wide angle and the close-ups. (00:13:25)
Continuity mistake: When Magnum is fighting the one yo-yo and a half at the gas station, the big one grabs him in a bearhug. Magnum's shirt is down straight, but in the closer view his shirt is caught up in the clasped hands of the giant and is raised halfway up his back. (00:09:25)
Continuity mistake: When Magnum, holding his pants just with his hands, screams that "YES" he and the well-bred lady did indeed meet, she is holding her hat in a different way between shots; the bow on the hat is up in the first shot, at 6 o'clock in the next. (00:11:15)
Continuity mistake: Continuity issues happen once Magnum gets back to the table with his buddies, discussing how hard he had been blown off. TC's financial newspaper is folded differently and is still or windblown depending on the shot. Easiest transition to pick the mistake from happens when TC reaches for the money for bet; the wind lifts the page, which is perfectly flat an instant later. (00:06:00)
Continuity mistake: Magnum offers to give the uppity girl some tour and introduce her "to some people." Wind flips through the pages as he says that, but the book she holds is perfectly open and still at the edge of the frame in the close-up. (00:05:20)
Continuity mistake: During the beach scene at the beginning, extras get recycled - look no further than the girl in pink/purple gradient bikini that runs from right to left a few times between shots. (00:03:45)
Continuity mistake: Higgins gets to the beach and lambastes Magnum for his "aggressively offensive attire" (on the beach, which is in fact absurd). During the scene, when the camera is on Selleck, in the background the weather is pretty cloudy, while in the wider angles there's bright sunlight on the beach and extras involved. (00:03:45)
Continuity mistake: Magnum gets out for a swim after the second sleepless night, carrying just a towel. He has a run-in with the lads, and spends all the time running away from them till Mac fetches him and they get back to the guest house. Magnum is now also wearing his Detroit Tigers cap and brought no towel back. (00:42:15 - 00:43:45)
Other mistake: In the opening credits, Clyde Kusatsu is listed as guest star playing "Colonel Ki." However in the end credits Robert Inouye (should be "Inoue", really) is "Colonel's Ky's driver." Ki seems a more plausible spelling, but it should be noted that in the actual episode, during the meeting when the Americans ask the General about returning the bodies buried in 'Nam, the nameplate of the absent Colonel says "Col. Ky Lan." (00:01:55 - 00:31:25)
Other mistake: The sunset Magnum comments on and is featured in the opening shot of the scene has nothing to do with the actual light of the rest of said scene. (00:08:40)
Visible crew/equipment: For some reason, Higgins is quite defeated by Magnum reading the lie he obviously is willing to publish, and snarls "Name it" in response to his request for more of Mr. Masters' belongings. On the far end of the wall on the left side of the screen you can see the shadow of the boom mike move. (00:07:30)
Character mistake: When Magnum looks at the pictures Higgins gave him, he sees one with a flare that will require him to ask Higgins to do some movie photography magic to remove it. However next to it there's a picture with just a slight less zoom that has no such flare. Magnum for no reason entirely ignores it while he only needed to grab a magnifying glass instead of begging Higgins and wait for the film to be developed again. (00:29:30)
Other mistake: Colonel Ky fires his gun at Magnum a first time when he is picking up the handkerchief. In the background, a woman in brown is walking peacefully. Cut to scared crowd all over the place. Magnum turns the corner and from the new cover shoots a couple times at Ky. Next shot Ky returns fire, but it's just another take of the first shot; the woman in brown is again walking where she was, and reacts to the gunfight only at that point. (01:30:40)
Continuity mistake: In the sudden 'Nam flashback, the helicopter is hit and everyone starts shooting. Rick in close-up is shooting holding the M16 with his right hand for support and the left hand on the trigger, while in the following POV shot the person shooting is doing it the other way around. (00:16:15)
Character mistake: Higgins holds his glass of brandy with Magnum's photos in the other hand and says "I don't know if you're pulling my leg, as you Yanks put it." It's really not an exclusively or typically US expression; in fact it originated in England. (00:27:35)