Continuity mistake: The opening of the show starts with Magnum driving off with the iconic Ferrari; however it has a license plate number, 56E-478, which is not the one seen in 99% of the show. It comes from the pilot episode, where the vanity plate ROBIN-1 had yet to be introduced.
Continuity mistake: Magnum comes back to the beach after some surf ski, where the prince struck a 'deal' with Ed Russler. Magnum's shirt is wet in two completely, and that's not a understatement, COMPLETELY different ways before and after John Saxon approaches. (00:28:30)
Visible crew/equipment: While Higgins is standing beside TC's hospital bed there's a boom pole and mic hovering low in the area of Higgins' legs, and it can be seen in the two wide shots from behind Higgins, especially when Rick mentions the noontime news. (00:06:40)
Continuity mistake: Rick tells (and shows!) Magnum that he's writing "a recipe for Veal Marsala for my mother back in Chicago." But the key plot element of 4-4 "Distant Relative" was that Rick raised his sister by himself, because Chicago was "a tough town to grow up in without any parents."
Other mistake: Fun gag but does not make sense; Magnum has a prolonged conversation at the bar (not a random brief chance encounter) with Lou Whitaker and Alan Trammel, and he, a huge Tigers Fan who in other episodes proved to be able to recognize obscure players from other past teams, needs the bartender to tell him who they were. (00:27:30)
Continuity mistake: For the first episodes (minus the plot), the opening of the series features the Ferrari with two different license plates. The opening shot shows the ROBIN-1 vanity plate that is in every episode but not in the most well known version of the opening (with the iconic Mike Post theme music used in all the other seasons), and the following shows the license plate from the pilot.
Other mistake: Twice in the episode it is explicitly said that Magnum's phone has been disconnected, and that Higgins checked with the phone company. Yet at the end, it turns out 'the lads' chewed on the cable. Surely the phone company wouldn't tell the estate manager that the line has been disconnected for billing problems (so, a well determined administrative issue with proper paperwork done) when it's a wiring problem.
Character mistake: The party is supposed to be "One of the premiere social events of the season", but the only people invited (Higgins knows for sure who is gonna come, so it's not like there's low attendance because of the weather) are a Prince from a fictional European state nobody knows about with his commoner wife, the editor of a poetry magazine that needs Robin's funds to survive, a sports star and Robin's accountant. 5 people in total, already all in Robin's pocket, and nobody else in attendance. While you could say that having royalty and a golden glove winner is certainly noteworthy, those people don't meet anyone else. Hardly a 'social event'. (00:04:00)
Continuity mistake: Magnum is bullied into going with Carol's lame plan. The very first shot of him and TC on the Ferrari on their way to block the drug lord shows TC wearing a white sweatband on his head he does not have in the rest of the episode; it's recycled from 1-13, All Roads Lead to Floyd, and you can even spot the car typical of that episode. (00:29:10)