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: 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: 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)