Continuity mistake: Magnum comes back to the beach after some surf ski, where the prince struck a 'deal' with Ed Russler. Magnum's shirt is wet in two completely, and that's not a understatement, COMPLETELY different ways before and after John Saxon approaches. (00:28:30)
Continuity mistake: Rick tells (and shows!) Magnum that he's writing "a recipe for Veal Marsala for my mother back in Chicago." But the key plot element of 4-4 "Distant Relative" was that Rick raised his sister by himself, because Chicago was "a tough town to grow up in without any parents."
Continuity mistake: During the paperboy run, TC stops the van and asks Benny a question. Benny was holding the paper vertically, but his arm is down in the next shot, and up again next, and so on. (00:32:40)
Continuity mistake: Magnum gets back to his pad and of course the kid everyone's looking for just crashed there. In the first shot, overhead, you can see that Magnum's coffee table features several magazines, and in the corner, at the same level, a bowl. Magnum fetches a can of beer and sits by Danny, but the magazines now are in a different line, with the bowl above them. (00:13:20 - 00:13:50)
Continuity mistake: Serious matters of Little League espionage are discussed as TC accuses Magnum. When he says "They beat Taiwan" he has not a hand on the cooler full of Gatorade with badly camouflaged labels, but he does then, right at the cut. (00:05:40)
Continuity mistake: When TC asks Benny (of course with no foreshadowing at all) "You don't wanna be someone else, do ya?" his van is parked in front of a hedge. Cut, and they are in front of garage doors. (00:32:45)
Continuity mistake: John Saxon hands Prince Danny's pic to the arcade manager holding it by the top left corner in close-up, but his fingers were on the top right in the wider angle. (00:41:20)
Continuity mistake: Magnum met the Prince 5 seconds earlier and already he has enough of him and says bye, about to drive off. Danny says "Hey", and at the cut the glove rolled from under the right to the left hand. (00:08:20)
Continuity mistake: Rick gets the odds from Magnum and then puts the car in reverse. His left hand is on the left part of the wheel, right hand at the cut. (00:07:25)