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)
Other mistake: The TV report about Magnum doing a Ready Player One backwards race, is shot from a perspective that would have required the cameraman to practically sit on Magnum's bike hitching a ride, in particular at the end. (00:48:25)
Factual error: Magnum takes part to an Ironman triathlon contest, but the writers did not bother to follow the correct order of the parts of the race, which would be swim, bike, and then run. Here he cycles last.