When Magnum is pursued by the beaten up car, after it goes over the cliff edge, he screeches his Ferrari to a halt, burning rubber from his tyres as he does so, leaving obvious black marks on the tarmac. However, after he drives off again, one of his pursuers climbs back onto the now empty road, which is also clear of tyre marks; it suggests that they filmed the crash, destruction of the car, and the climb back to the road before they filmed the scenes with Magnum.
During the Vietnam flashbacks TC and Rick are shown to be flying in a Bell 206 JetRanger helicopter. Their unit VMO-2 only flew UH-1 Huey and AH-1 HueyCobra helicopters, and OV-10 Bronco fixed-wing airplanes during the Vietnam War, and the JetRanger was only operated by the Army, never the Marines, as the OH-58 Kiowa.
Dan Cook's right eye twitches slightly when his head is rinsed during his autopsy.
About half way into this episode, the bad guys in a rusty car are following Magnum. Magnum takes a turn that would take him down Kslakawa into the heart of Waikiki. They say he is getting on the freeway, which is where Magnum's car amazingly jumps to.
After Magnum "steals" the Ferrari, he slides the Targa roof back then takes off. With no cutaway, the roof is nowhere to bee seen, this kind of roof has to be lifted off then put vertically behind the seats. There had to be 1 or 2 people to quickly take it away.
When Ensign Healy is mentioning a Japanese A6M fighter that was supposedly shot down during the attack on Pearl Harbor, he says that it was shot down 30 years prior, in spite of the attack on Pearl Harbor happening nearly 40 years prior.
Soldiers in Vietnam would not be fighting wearing berets; they would be wearing helmets.