Revealing mistake: When Magnum socks the detective, The Turk starts going down with the punch almost before Magnum swings. (00:33:35)
Plot hole: Magnum and Rick manage to switch Yuri with Fillipovitch through sheer magic; they base their infiltration on a little boat barely big enough to contain the two of them, with no room for them to hide the uncooperative Russian, plus we see most of their movements including them climbing up. It's simply a 'shocking reveal', but it's not setup in any believable way.
Factual error: The whole episode begins with the premise that a Soviet pilot would fly his MIG aircraft all the way to Hawaii to defect to the US from the USSR; while the aircraft of this episode is fictional (MIG-30), it still is at unreasonable distance for a military jet fighter of its era.
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: In the scene in the study at the beginning of the episode, Magnum just ran from the ocean to the house, but his swimming trunks are barely wet at the border of the leg. (00:05:40)
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)
Continuity mistake: Asking for camera film was a bit much, so Magnum skedaddles with a cheeky grin before the lads chew him off. As he makes his exit, he is holding the bag in a different way, with the strap across instead of straight. (00:08:10)
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)
Continuity mistake: After being negligent with his paying customer tossing the evidence in the ocean, Magnum is taking pictures of a ship. From behind, he's taking pics with both hands on the camera, from the front, he's handling it with just the right one. (00:10:25)
Visible crew/equipment: After Magnum shows TC and Rick the photograph of Michelle, TC suggests that he and Magnum go for a walk, and as Magnum stands up the white T-mark is visible under his chair. (00:10:30)
Deliberate mistake: Magnum spots the fateful brunette on the yacht. During this scene, a couple times he sees her with the exact angle of the camera zoom when he just pulled away from it. (00:11:00)
Audio problem: Magnum approaches Rick and TC at the table playing cards. TC's voice says "Fourteen bucks up on ya", but Roger E. Mosley's lips don't match and are the audio is Out of Sync, since he continues moving his mouth while Rick is saying something. (00:14:00)
Continuity mistake: Rick checks out of the photo Magnum hands him. In the background, cards are scattered on the table. The next time we see the table a couple cuts later, the two of hearts changed position, now being on top of the scattered cards, and it is in yet another position during TC's close-up. (00:14:35)
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)
Continuity mistake: When TC and Magnum have the conversation on the beach, extras are constantly recycled; obvious example is the girl with a bandanna and a red bikini, appearing behind both too. (00:17:30)
Continuity mistake: When Gen. Hu is teasing Col. Ky about his need to justify his lack of results, the shadow cast on his chest changes heavily with the camera angle. (00:21:15)
Other mistake: The US delegation pops from behind some trees with military copters that are explicitly presented as deafeningly noisy; it's just silly and internally contradictory. Even if we forget how underplayed helicopter noise often is in Hollywood, here we go from zero to thunderous in a split second. (00:21:40)
Other mistake: Magnum and his bride seek shelter under table during the bombardment; if it happened the way it is shown, with a model completely torn to pieces, and with flames in frame during the first table shot, they would surely not be able to stay there, nor would have taken refuge there to begin with - if the roof did not kill them already falling on them. (00:25:10)
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)
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)