Continuity mistake: Magnum is stretching after his morning jog in front of a bottle of Coops that turns between shots. (00:02:35)
Continuity mistake: TC is trying to convince Magnum at the beginning of the episode, and tells him "Bet you can do it." Ten seconds pass and there's a new reaction shot on him laughing at Rick's little Higgins impression. Thing is, those few seconds a large ship that was present in all the other previous shots disappeared at the horizon all of a sudden, and there are fresh slipstreams showing that it is a much earlier or later take. (00:03:05)
Continuity mistake: TC tells Magnum "bet you could do it" when Magnum puts down his beer. Next shot and Magnum's hand is suddenly around the beer bottle again. (00:03:05)
Other mistake: Magnum tells Higgins he has just twenty-three hours to solve the case when both the clock at the Nest and the one at the Honolulu Lulu's Pool Hall show it's half past four. Magnum though accepted Babs' case around 11:30 AM ("11:29 at the tone", Rick jokingly said). (00:07:35)
Continuity mistake: Magnum and Babs walk away from the phone he greatly amused Higgins with. In the background, the bar clock shows 5 o'clock, when it was 4:31 merely seconds before. (00:08:40)
Continuity mistake: The scene when Barbara Terranova murders Magnum at billiards is shot with zero regards for continuity, just filming shot after shot even when the balls' positions do not match at all. Just look at the opening shot botched by Magnum; most balls are cluttering the middle of the table, but Babs takes her first shot shocking Magnum on a largely clean green rug. (00:09:30)
Continuity mistake: Magnum tells Barbara to go to the bathroom leaning against the windshield; his hands is turned in different directions depending on the camera angle. (00:13:30)
Revealing mistake: Magnum manages to shake off the 'government guy' by putting his car on a jack while Babs provides a distraction. But if you check the moment when the guy gets on the car, the back wheels are in frame and not at all off the ground as the clever ruse needs them to be. (00:14:40)
Revealing mistake: Magnum neutralizes the pursuer at the gas station jacking his car. In the close-up of the wheels spinning with no traction and then stopping, the hubcap is in pristine condition, but in the next one, it sports a dent already from a previous take. (00:15:20)
Revealing mistake: When the guy tricked by Magnum gets out of the car, check out of the very right side of the frame. You can actually see the hand of one crew member releasing the garage jack's lock, so that, when the car is kicked, the relatively light impact is enough to release the hydraulic lift and make the car comically bounce back on the ground. (00:15:25)
Other mistake: The license plate Magnum tells Rick to check out ("55 678") is totally different from the AYX 470 the guy was actually driving. (00:16:35)
Continuity mistake: The morning after TC and Babs sealed the deal involving him, Magnum goes out for a swim. In the first shot, when he turns around to tell Babs that he's not doing her ridiculous knee to chest routine, the towel around his neck shows no half-squares. In the rest of the scene, the towel is folded so that there's half a square easily recognizable. (00:20:00)
Continuity mistake: Barbara Terranova is biking behind Magnum when the golden teeth man and his buddy stop her. She screams "Magnum!"; look at the sweatstain on his back. When a few moments later he runs in to beat up the aggressors, the stain got smaller, or rather, oddly narrower, not being as wide on the neck of the shirt as before. (00:23:00)
Continuity mistake: Babs finally produces a picture with Roger. In close-up, Magnum is holding it by the corner, while he had his hand at the bottom in the first shot. (00:25:20)
Continuity mistake: Babs tells Roger "He's a private investigator" pointing at him with the same hand she had on his shoulder, and that is still there in the reverse shot. (00:31:40)
Continuity mistake: When Magnum protests that TC is "killing him" with his too much vigorous toweling, TC is wearing his baseball hat backwards, while it's worn normally in the previous and following shot. (00:39:20)
Continuity mistake: At the checkpoint after the swimming section, Magnum has to get out of the speedo and put on dry running shorts. He does so, but in the shot where Rick is powdering his feet and putting socks on him, he's still wearing the wet speedo. (00:39:40)
Continuity mistake: When Rick is helping Magnum after the swim session, he's putting the sock on him twice (although he did not finish the first) and the shoes on the ground are in radically different positions between shots. (00:39:45)
Continuity mistake: Magnum leaves the first checkpoint with the number on his back that covers entirely TC's sponsor logo - later in the race though he wears a different race bib that puts the logo on display. (00:40:15)
Revealing mistake: During the jogging phase, which may not be hazardous but surely is defatigating, Tom Selleck is replaced consistently and noticeably (except the close-ups, of course) by his stunt double Tom Lupo. (00:40:35)