Continuity mistake: Higgins' hand motion when he whips out of the cigarette case is incoherent between the various shots. (00:05:40)
Continuity mistake: When Magnum reports that he narrowed the possible spy candidates to those in marketing, his hands are crossed over - but in the next shot, he is crossing them again. (00:06:40)
Continuity mistake: Magnum and the corporate executive are having a chat after the board meeting. Throughout the scene, the same extras (starting with a man in a blue shirt and camel shorts, a man with a brown pattern shirt, a woman with a baggy sand dress) walk back and forth over and over in the mall or behind them at the tables. (00:08:00)
Continuity mistake: In the very brief dinner when Claudia tells Rick that it's over between them, she casts a shadow behind her in close-ups, all the way to the left in the other shots. The difference in ambient lighting of the whole table spot is significant too. (00:18:20)
Continuity mistake: Magnum is hunched over the Ferrari opening the door when the car first tries to run him over, but in close-up Tom Selleck is standing tall. (00:22:50)
Visible crew/equipment: When Magnum asks the security guard to call Mr. Randolph so he could enter the building, it then cuts to Randolph's office and as the camera turns we can see the white T-mark on the carpet, between the desk and window. (00:25:55)
Continuity mistake: Magnum is in James Randolph's office and 'the new guy' is talking to him. He says he disagrees on Magnum's hypothesis; in the transition both him and Randolph have very different positions, with Randolph's hand on the glass and arm raised differently, and J. Weston Reese's arms from crossed in front, to his pockets. (00:26:45)
Continuity mistake: Randolph puts the secretary on hold as Weston Reese tells him his plan to keep Magnum a target. Randolph's arm is in a different position on the desk depending on the camera angle. (00:28:25)
Continuity mistake: Higgins hobbles towards the club's beach bar in his horrid state (you'd think he wouldn't be caught dead looking so ridiculous) and starts reminiscing about the war and trying to mooch a cigarette. In the background, the same blonde with a black bikini hops over the wall twice, and same for the Asian with a blue/black swimsuit. Moreover, a girl in a red bikini and yellow towel keeps making back and forth walks by the surf on the beach. (00:29:30)
Continuity mistake: Rick tosses the lighter on the table when Magnum shows up tobacco-blocking poor Higgins. The lighter is in a spot on the table next to a paper cup that was never there and is gone after, and the lighter moves too. (00:30:45)
Visible crew/equipment: While Higgins is on the road trying to complete his jog, when Magnum pulls up alongside an exhausted Higgins, the reflection of the reflector screens is visible in the triangular window. (00:32:30)
Revealing mistake: Chased by the bad guy who shoots over 9 times, Magnum makes a sharp, almost "U" turn; the car slows down during the turn, enough for the viewer to appreciate how thoroughly unlike John Hillerman his stunt double is, with his head full of hair. (00:33:10)
Visible crew/equipment: At the airport, while Randolph holds a gun on Rick during the standoff Claudia shouts out, and when Rick falls to the ground just as Randolph starts to flee, the arm of the boom operator and the boom are visible at the right side of the screen. (00:44:00)
Revealing mistake: When Magnum chases after Randolph at the airport tarmac and finally catches him, there's an outline of elbow pads on Magnum's sleeves. Earlier, there was a shot from behind Magnum as he pulled the gun from his waistband, and his sleeves were normal.
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?
Other mistake: A big deal is made of Magnum wearing a suit, both by Higgins and by Magnum himself when he speaks to others. You'd expect then this to be the first time we see him donning such a formal, wear and head into a corporate meeting, but he wore in fact a suit for a long portion of screentime just two episodes prior, in Ghost Writer (2-11).