Revealing mistake: In the opening of the second third of the season (the one with the iconic Mike Post theme) there is a brief scene with a car propelled in the air by an explosion. It's an outtake from the pilot movie, since the banged up car is very recognizable, but it's also easy to see why it was an outtake; you can easily see cables used to make the car fly in the air. Also, that car was not in an explosion in that episode.
Other mistake: Forgetting the absurdity of a kid who's never been on a horse before that can just hop on one and gallop all night long, the stuntman riding Agatha's horse when Higgins and Magnum watch them fade into the night wears a striped shirt; Benny in the morning is still on the horse, on the run, but has a sports jersey with a very different color pattern, basically bi-color with the full bottom half powder blue. (00:36:50 - 00:38:15)
Continuity mistake: Magnum is at the guesthouse with Luther. He grabs a Coops beer from the fridge, but does not close the cabinet door. Which is closed when Luther says he's gonna go get Artie. And then open again when Tom Selleck gets up and is in the same shot as Eugene Roche. (00:19:05)
Continuity mistake: Magnum during the surf ski race wears two different hats; first we see his Tigers hat (white logo), but then he has the yellow logo Da Nang hat - which he lost in the ocean during the season opener when the two "turkeys" capsized his craft. (00:42:00)
Revealing mistake: Magnum finds the unpleasant surprise of a large scratch on Robin's Ferrari. In close-up he runs his hand along the "bloody gouge", as Higgins later calls it, but it's a badly constructed prop; look at the turn signal, tiny and circular, nothing like the larger rectangular one of the car. (00:23:40)
Revealing mistake: The closing shot of the episode shows the lookout point platform where the suicide attempt happened...but also, below it, you can catch a glimpse of an additional platform, and a rope probably used for safety reasons as well. Needless to say, it was not featured in the dramatic shot of Holly looking down into the abyss. (00:46:55 - 00:47:40)
Revealing mistake: Sam takes off from Van Nuys on his Super Stearman. We'll see him in Waco do all sort of acrobatics...but when he is first shown in the air right after talking with Richard Roundtree, you get a glimpse of another cockpit where the real pilot is, strapped with the safety belt that pokes in frame. (00:20:30)
Continuity mistake: The car chase from the gas station to the banana plantation happens with the mobsters driving two cars passing as one. The first car is a Ford Sedan with single headlights and front and back license plate 3F-2890, but the car speeding up in most of the shots driving through the long roads is a similar model with double headlights, different grill and without a front license plate (7F-7594 is the back one, but you may need to freeze-frame for this last detail). (00:21:30 - 00:22:25)