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)
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.
Plot hole: Magnum is amazingly naive in this episode, blindly believing the story about Tracy Spencer being a cop against every possible evidence of the contrary. This buffoonery aside, Tracy saves him from the two girls identifying herself as a cop, but a couple scenes later they both go meet their boss and try to set up a sting passing off as dealers of stolen goods. That does not make any sense.
Forty Years from Sand Island - S3-E17
Plot hole: The culprit is in cahoots with the man that Magnum is trying to expose as WWII war criminal, and fears nothing from him, as he even explains to Magnum later; in fact he is his goose with the golden eggs. Yet he, a politician, kills his guy in broad daylight, for no reason, running the risk not only to be caught red-handed, but also more logically to be linked to him due to the investigations that will unveil the deceased as one of his major supporters. Instead, he does not touch Magnum, someone he has no connections with and tons of potential enemies. Let's not forget that the main motive that pushes Magnum to investigate is his assumption that someone wanted to kill Higgins, which is not the case, and the culprit knows that.
The Case of the Red-Faced Thespian - S4-E12
Plot hole: The plot of the episode has a big reveal that tricks the viewer making zero sense; the victim is alive and well, but there's an ambulance, they bring the victim away, and Magnum spends most of the episode in the noble effort of saving Higgins from a murder accusation. Magnum mentions "I figured I still had about a half an hour before Tanaka returned with a warrant for Higgins' arrest." even in his internal monologue, so it's not that he was trying to hide the fact from other characters.
Plot hole: The plot of the episode is nonsense. The boss of the company knows that Magnum made no progress and is on the wrong track, since he suspects someone in Marketing - it should also be noted that Magnum is mystified knowing that the President has the access codes, but he himself has them, and it would be a given to learn who has the various codes as first thing in a security analysis like he conducted. Yet for a couple weeks this Prez guy sends his wife to just sleep with the PI's friend, for...no discernible reason, other than create a diversion he did not need and that hinges on events and reactions that non only he couldn't predict, but also have nothing to do with facilitating his espionage, considering also that a more competent security firm is hired right after. Likewise, why would the guy from R&D try to "scare Magnum off" doing an attempted murder that is sure to get him arrested when he knows Magnum is focusing on the wrong department?
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.