Continuity mistake: Approaching the ship at the beginning of the episode, TC's chopper is the N58243 model, with the flotation skids. When he actually lands on the bridge though, it's N1095A. (00:02:05 - 00:03:00)
Revealing mistake: When Magnum wakes up finding the tape recorder on the pillow, his collarbone scar shows the contour of the prosthetic patch. (00:13:20)
Continuity mistake: When Magnum is pouring beer and tomato juice in the blender, bottle and can switch hands - look at the blender's jar and its handle. (00:14:20)
Continuity mistake: Magnum is dosing tabasco into the thing his girlfriend makes him prepare; notice he's wearing his team ring with the proper orientation (two arms of the cross of Lorraine closer to his hand). When he pushes the button of the mixer, the ring is upside down. (00:14:40)
Continuity mistake: Magnum is following the icky instructions for a protein drink left by his unseen girlfriend with the golden voice. Somehow from eggs, flat beer and tomato juice, the result is a green mix. He is blending it in close-up on the table (the wood texture is a tell), but he recovers the goop from a different piece of furniture with a sink. (00:14:40)
Continuity mistake: The foul concoction Magnum prepares based on his girlfriend's recipe fills the glass at a different level depending on the angle before Rick's arrival. (00:15:00)
Visible crew/equipment: After TC is taken away by the Marshals, it cuts to Magnum and Rick standing in front of the map with the Coast Guard personnel, and when Neil begins to explain where they intercepted TC, a white T-mark is visible on the floor. (00:18:35)
Revealing mistake: On the docks, Magnum saunters towards a payphone. The phone is not exactly a sturdy or well made prop, because it wobbles even before Magnum touches it. (00:26:40)
Continuity mistake: During his scuffle with TC, Magnum is wearing the same white tennis shoes he was wearing in the ship scene in some shots (closer angles generally), and dirty, chunkier sneakers in others. (00:36:40)
Audio problem: When Magnum is pushed against the metal shelves by TC, a big clunking sound is dubbed in, but you can see that the shelves and their content are not wobbled in the slightest and Tom Selleck jumped himself against them using his hands to impact in perfect safety. (00:36:40)
Continuity mistake: During their fight, Magnum in a close-up slams TC on a table. A chair is lying on the floor by the table; that chair will be toppled over only in the following shot. (00:37:00)
Revealing mistake: In the longshot of the fight when the phone begins to ring, the stuntman replacing Roger E. Mosley is quite visible. (00:37:05)
Continuity mistake: Frustrated by Joey's deception, TC tosses the bag of heroin on the dresser, and it ends up on top of a box. In the next shot, it changes position, being off the box. (00:40:25)
Revealing mistake: When the bad guys try to escape from the warehouse, multiple tiremarks of their highly unusual maneuver (a sharp turn that leads away from the door, in that precise spot) are already visible on the ground, no doubt from previous takes. (00:44:45)
Plot hole: The villains need to smuggle a bunch of drugs in the island. Their brilliant plan is; bring along a junkie who is wanted by the Navy but happens to have a friend who flies a chopper, trust that this guy will risk his life for the junkie to go get him at night and smuggle him in the country, and load the guy's heli with drugs while he's on the ship to fetch the junkie. Then, as he's flying the helicopter full of drugs, rat him out to the coast guard so they arrest him, ruining him so his chopper gets on auction, and they can buy the chopper back, with its load of drugs. There's just so much wrong with this plan already (why do everything so he's caught? The drugs can be retrieved later at night from the super-easy-to-reach compartment), add to that the fact that they even give as send-off to the junkie a giant bag of drugs, worth easily in the 6 figures; if they catch a drug addict with such a load of dope, they are bound to search the chopper - but really, they should have anyway.
Factual error: Justice in Hawaii works at a breakneck pace; TC is jailed and goes on trial instantly, which is fine, but also his impounded chopper goes for auction within a couple hours as well.
Character mistake: Twirling their moustache at the success of their operation, the villains say that the heroin is worth 10 million dollars. When Rick looks at all the drugs, he says it must be worth "a couple millions."