Continuity mistake: Magnum pours a scotch to his aspiring client, tosses in the other room whatever was occupying the chair, and sits down. Yuri Dolgof comes closer to convince him; during this part of the scene, Tom Selleck (or his stand-in) has the arm raised, leaning against the hand to listen, but in the frontal views he just has his arm on the armrest. (00:11:00)
Continuity mistake: Yuri and Magnum are stalking the athletes from their observation spot. When Yuri says "Her English is very good", his right hand is by Magnum's side. Next shot and it's behind Magnum's other shoulder. (00:13:00)
Factual error: The first attempt to extract Nina fails. The messy and grizzled KGB agent says then, in captions (hard subs); "Excuse, Mikhail Fillipovitch." Filipovic, maybe, surely not with the double L; you can also hear in the pronunciation there's no double. (00:15:00)
Continuity mistake: Magnum is teasing Higgins about the "toys" and sits in front of the Austerlitz model. Higgins holds the statuette in different ways (by the base, or with a finger on top) depending on the camera angle. (00:22:35)
Continuity mistake: Higgins is stunning comrade Kalugin with all his blabbing; in the view from Magnum's POV, the two are sitting in an area under direct sunlight, contrary to the rest of the scene. (00:27:50)
Continuity mistake: When Rick in disguise is in front of an athlete's bungalow and questioning the size of her extra 'chromosome', the fake Press pass on his chest is angled differently between shots. (00:29:00)
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)