Other mistake: Magnum is 5 years old when his dad leaves for Korea, and is 6 by the time he's dead, coming back in a coffin on July 4th 1951. That does not work with the birthdate that appeared on the driver license in Memories Are Forever, episode 2-5, which is even abundantly referenced here with footage being re-used (Magnum's wedding party with bombs, and making love to his wife years later in the guest house). He was born January 5th 1946 in the document shown in close-up there.
Other mistake: Rick breaks off his hot date and goes searching for Magnum driving his boat for a long while -before- contacting Higgins to see if Magnum is missing at all. It also is the middle of the night and close to dawn (Magnum has to wait just one hour before the sun comes up) but Rick is still drinking wine (but not drunk) and hasn't even touched second base with the girl despite the fact that they were mixing wine and going below when the sun was still up.
Other mistake: Higgins says he hasn't seen Magnum (or his surf ski) "for two days", but Magnum left on the morning of the 4th, and has been in the ocean for 20 hours total. He spends the 4th on his own, but on the 3rd his friends and the ever-seeing majordomo of the estate should have gotten any sign of his presence.
Luther Gillis: File #521 - S4-E2
Other mistake: The guesthouse scene with Magnum and Luther opens with a prolonged gag about Magnum "finally" getting an answering machine. It is said that it's the first time he gets one. But in the season 1 finale, "Beauty Knows No Pain", Magnum's client Barbara Terranova commented that the message on Magnum's answering machine mentioned the club. (00:03:25 - 00:18:00)
Luther Gillis: File #521 - S4-E2
Other mistake: The policeman opens the closet door in the most transparent "a corpse is going to fall off from here and I know it" way, stepping away from it and even looking down where the body will drop. (00:05:45)
Luther Gillis: File #521 - S4-E2
Other mistake: Luther decks one of the old ladies with a punch. When he strolls past them after slipping Magnum a mickey, he looks back at them, and one in particular, who is sporting a patch. It is not the same lady he punched earlier. (00:17:35 - 00:21:30)
Luther Gillis: File #521 - S4-E2
Other mistake: Higgins is on the lawn doing his martial arts demonstration, so there's nobody to open the gate that Luther passes in reverse gear. (00:21:55)
Luther Gillis: File #521 - S4-E2
Other mistake: For the first 2/3 of the episode (up until their second prison visit) Magnum is wearing the same watch he had been wearing for the previous three seasons, with a leather strap. For the last part of the episode he wears the pepsi bezel watch with a metal bracelet that he inherited from his father and was the focus of the previous episode and will be his regular watch for the rest of the show, in kind of a retcon.
Other mistake: The guy rummaging through Waldo's stuff in the room does not get alerted by their loud chat outside the room, nor the door unlocking, not even their steps; he just turns around suddenly when they both are in the room, standing still in silence and looking at him, who has his back turned to them. Must have had eyes on the back of his head. (00:09:10)
Other mistake: Lee has an Atari 830 Acoustic Modem, which has on its front panel an instructional "cord side" illustration, showing the proper direction for the phone cord when the phone handset is secured in the top two cups. The telephone's cord must be placed at the right side in order for the acoustic coupler to work, but in both Lee's and Magnum's closeups, the phone cord is on the left side, but the acoustic coupler works properly. This is impossible. Also noticeable in closeups is the covered brand name of Atari on Lee's devices. (00:24:20 - 00:27:20)
Other mistake: When Magnum makes a typo with the "Torpo Corporation" name, he types "Torbo"; B and P are nowhere near. And to fix it he types a B, and backspaces. That's not how it worked, ever. (00:27:40)
Other mistake: Higgins is outraged about a precious 1923 sketch being stolen by Rick's friend. Then again, that invaluable (as he puts it) piece of paper was stored in an open rack, rolled up with a rubber band. That's hardly how such an antiquity would be preserved by someone who finds it this valuable.
Other mistake: Magnum wakes up because Agatha and Higgins are playing with their model planes that loudly buzz in the air. He opens his bedroom window and here they are, by the guesthouse, with a direct view and Higgins waving at him. He then gets out to give them a verbal beating, and he's coming from the main house area. (00:02:15)
Other mistake: Rick enters Wendy's room shouting like a madman, and then reaches the bedroom door trying to turn and pull the knob. He bangs the door, calls for Magnum's help, and both then bust the door open. In all that, the guy going through Wendy's underwear and bed sheets is still unfazed and stops what he's doing merely when they almost fall on him. (00:18:00)
Other mistake: The opening sequence featuring a blonde in an orange bikini showering on the beach is recognizable as reused from a kidnapping scene in one of the early episodes of the series, 4 years before; China Doll. (00:01:50)
Other mistake: Magnum rewinds the answering machine tape hitting the opportune button just once, and it plays on its own the exact bit he needs to listen to, without any intervention on his part. (00:36:20)
Other mistake: Magnum and Vivian are not listening to the TV at loud volume (they have a quiet time watching and talking without raising their voice), but Higgins, all of a sudden hears it all the way from the main house and is greatly bothered by it.
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)
Operation: Silent Night - S4-E10
Other mistake: The three friends mistake Higgins' footprints in the sand for a pirate's. They find him and they have their explanation; Higgins is carrying a cane and some palm leaves; dragging the palm leaves, he involuntarily erases the prints of his foot, while the cane leaves a circular print akin a wooden leg's. That makes no sense, because as it is shown, Higgins is holding the cane in his right hand, and dragging the palms with his left; he'd wipe the prints of his left foot, if anything. And yet when Rick pointed at the prints, it was obviously a left footprint. (00:18:20)
Operation: Silent Night - S4-E10
Other mistake: Higgins ask for the hacksaw from TC's toolbox. In 30 seconds sharp (no pauses in the dialogue), Rick brings it to him. So the wrecked airplane and the chopper are 10 seconds apart, in a thick forest. That's quite a bit uncanny. (00:24:15 - 00:24:45)