Don't Eat the Snow in Hawaii - S1-E1
Plot hole: The clock at customs signals it is 9:05 AM when Lt. Dan Cook arrives at Hickam. Magnum narrowly misses him. Then he goes back home...and it is night. There is no reason why Magnum would have spent the whole day out of the house, especially never checking on his fraternal buddy he was supposed to chaperone to begin with.
China Doll - S1-E3
Plot hole: Choi spends less than a minute inside the antique store. Magnum and Mai Ling left another minute earlier, tops - you could see Choi making his way to the store in the same street shot when M&M were leaving. And yet, TC's chopper is already passing over Choi's heads when he asks where the girl and her precious belonging are. Of course it makes no sense especially considering that TC had landed on a beach spot, tied down the rotor, argued with Magnum...it'd take minutes to take off, and Magnum and Mai Ling were in no rush at all, not making a run for it. (00:13:00 - 00:14:45)
China Doll - S1-E3
Plot hole: Choi is a single guy with no help from anyone else no superpowers (just a rather deadly fist), always shown on foot and yet he is able to follow Magnum always. He has to ask for directions at the beginning of the episode (with the store being about 3 doors away) so he's not omniscient, but somehow he is able to show up wherever Magnum goes, including where he just drove his super fast Ferrari, or when he's getting free helicopter rides.No explanation is attempted or hinted.
Thank Heaven for Little Girls and Big Ones Too - S1-E4
Plot hole: "Three Tahitians", one of the masterpieces from one of the most famous post-impressionist painters in the world, is authenticated by an ordinary school teacher. Because that's the person for this multimillionaire job, obviously. (00:25:20)
Plot hole: Towards the beginning of the episode a peculiar arrangement is presented; Magnum has to share the guest house with two stewardesses, Mandy and Suzie. The night of the party, they both go for a swim. Mandy is involved in a shooting, and following scenes include her resting at the guest house. Suzie is never heard from since. She does not have a place to sleep; it is made clear that the main house has not been arranged yet for that purpose, the Brigadier and his escort have to leave first. She is not there in the morning. She just vanishes.
Plot hole: The villains need to smuggle a bunch of drugs in the island. Their brilliant plan is; bring along a junkie who is wanted by the Navy but happens to have a friend who flies a chopper, trust that this guy will risk his life for the junkie to go get him at night and smuggle him in the country, and load the guy's heli with drugs while he's on the ship to fetch the junkie. Then, as he's flying the helicopter full of drugs, rat him out to the coast guard so they arrest him, ruining him so his chopper gets on auction, and they can buy the chopper back, with its load of drugs. There's just so much wrong with this plan already (why do everything so he's caught? The drugs can be retrieved later at night from the super-easy-to-reach compartment), add to that the fact that they even give as send-off to the junkie a giant bag of drugs, worth easily in the 6 figures; if they catch a drug addict with such a load of dope, they are bound to search the chopper - but really, they should have anyway.
Plot hole: After the farcical scene with Rick and TC playing Asian goons, Magnum says in his trademark voiceover; "I know what you're thinking. After the phony beach attack, I should have said goodbye", etc. But the staged attack was in a back alley, in the streets. There are a couple of deleted scenes that pop by in the teaser and never made it to the actual episode, plus an actual beach attack happening later, so it's hard to say what Magnum was referring to, but in the episode as shown, makes no sense. (00:12:50)