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.
Other mistake: The commanding officer to enter the control room passes in front of two signs which, even with different sizes, say the same thing - but the one on the wall mentions a "Wheeler airbase" (which actually exists), the one on the door a "Delber". (00:02:00)
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.
Continuity mistake: The opening shot of the intro shows the takeoff two planes with a black nose and USAF written under the wings. When they are in flight later after the control room scene, stock footage is used, because now the planes have "MARINES" written above the wings, followed again by a close-up, this time of a white nosed airplane (or mock-up) with a recognizable number 23 that was absent before. (00:01:30)
Continuity mistake: During the credit sequence, at "Directed by", the pilot undoes the seatbelt. Under the suit, his left wrist reveals the presence of a watch, which is at the right wrist when he gets out of the plane. (00:05:15)
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)
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: 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)
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: 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)
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: The close-up of the battle of Sebastopol - or rather, what Higgins mistakes as such - sees Rick's hand on the sand, by the shell. The hand is not in that position in the other angle. (00:07:40)
Continuity mistake: The MIG pilot is preparing to get out of the plane. There's a close-up of a young and a bit tense soldier (or "soldier", since the extra looks quite unconvincing and not handling the weapon very confidently) wearing glasses. The strap of his weapon is firmly pressed between his fingers and the gun, but in the wider angle the strap is sorta slipping away. (00:05:15)
Factual error: During the aerial maneuvers, the so called Mig-30 (no such plane exists) is easily recognizable even from those who aren't aviation buffs as just the same plane as the two US ones intercepting it, but with an opportune paintjob. Especially obvious during the credit roll for Jeff Pomerantz, when the three of them fly slowing down for the landing, and in formation. (00:04:00)
Revealing mistake: When Magnum socks the detective, The Turk starts going down with the punch almost before Magnum swings. (00:33:35)