The Case of the Red-Faced Thespian - S4-E12
Plot hole: Magnum is incredibly slow to unveil the charade at the base of the episode; he does it based on something marginal (Robin Masters does not do "research" for his novels), but he completely overlooks the key plot point of 1-17 "J. Digger Doyle" was that he does not use a typewriter, but he dictates the novels.
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.
Continuity mistake: Magnum and TC hi-5 at the beginning of the episode. The football bounces at distance from TC in the first shot, but it's right at his feet after their hands clapped. (00:02:00)
Revealing mistake: TC runs into Higgins avoiding him in the front view with John Hillerman, and hitting him when he's replaced by a stuntman. He also is sprawled face down on the lawn with one or both arms up. (00:02:45)
Continuity mistake: Drunk Carol is telling Magnum why she was fired. As she says "They took it away from me", her hand is in front of Magnum's, and yet it is on top of it at the cut. (00:06:00)
Continuity mistake: Magnum begins to open the safe; the sensor with the red wire is in left position, black wire in right position. When he removes the sensors, it's the other way around. (00:23:00)
Revealing mistake: When Carol and Magnum jump from the terrace, you can see her land way too close to the edge of the garbage truck container; the stuntwoman's foot hits it in fact, and one of her shoes ricochets in the air. The stuntwoman picked up an injury, obviously, but Carol is unscathed and complains just about the suit getting dirty - when at the very least she lost one shoe. (00:25:30)
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)
Other mistake: Finally the gang is set free; the policeman says "Your bail arrived." Magnum asks "Carol Douglas?" But Carol's last name is Baldwin in the other episodes she's involved in. (00:35:30)
Visible crew/equipment: While Susan and Magnum are locked in the vault, when Susan pours the last of the wine into Magnum's cup and in following shots, the shadow of the moving boom mic is visible behind Magnum. (00:33:15)
Visible crew/equipment: When Magnum gets the bank vault door open he rushes to get Susan, and the boom mic moves around at the top, center of the screen. (00:38:05)
Continuity mistake: When Magnum and Rick find TC's office wrecked, Rick picks up a brochure and holds it out to Magnum in his right hand, with the team ring on his finger, but in the next closeup the ring has vanished. (00:41:50)
Continuity mistake: When Rick and Alexis try to escape in the chopper the baddies stop them, and when two of them leave with Alexis in their car, the rearview mirror repeatedly vanishes and reappears. (00:46:10)
Let the Punishment Fit the Crime - S4-E17
Visible crew/equipment: While Magnum is straightening up the guesthouse for Sally's visit, first Higgins shows up followed by Sally, and during this scene the back tape mark is visible on the floor near the round rug by the stairs. (00:19:20)
Holmes Is Where the Heart Is - S4-E18
Continuity mistake: While we hear Higgins in voiceover as the flame is moved closer to his hand, there is a segue to Magnum's voiceover as he reads the typed words of Higgins' memoir, which we see onscreen. The problem is Magnum reads, "I knew I had no information to give them," yet those words are not actually typed on the paper. (00:39:15)
Visible crew/equipment: After Magnum and Emily are shot at while in the parking garage, it cuts to Higgins telling Magnum that it wasn't his fault, and as the camera moves the actor's white tape mark becomes visible on the rug, beside his feet. (00:33:55)
Visible crew/equipment: During Rick's "demented mind" version of the story, when he and the pig masked baddie walk into the office the white T-mark is visible on the carpet, where the baddie stands. (00:15:00)
Echoes of the Mind: Part 1 - S5-E1
Visible crew/equipment: When TC and Rick are at the club while TC is doing the crossword, in the shot facing both of them just as TC mentions the lady mud wrestler, the lowered boom microphone's pole can be seen hovering beside Rick, at the left side of the screen. (00:05:50)
Echoes of the Mind: Part 1 - S5-E1
Continuity mistake: When Higgins hands the old album to Magnum, there's a closeup of the photograph of Lady Ashley, but in the wide shots no such photo exists on the album's open pages. (00:22:05)