Other mistake: The accountant first, then some minutes later the prince and princess arrive at the estate. They are bone dry despite the hurricane outside complete with pouring rain noises and strong winds. (00:05:35)
Other mistake: With power out Magnum somehow lights the gas stove with the knob, which is electric. Should have used a match. (00:26:40)
Other mistake: The killer is finally in action; they get a semiautomatic with a silencer from a case, then they do an ominous gun-in-hand walk bit (filmic stereotype where someone just walks with a gun out for no reason instead of concealing it). The shadow of the gun there though shows no sign of a silencer. The killer shoots indeed with a silencer - the audio implies that - but in the shadow you can see it is now a revolver. (00:44:20)
Other mistake: The Prince and Princess of Turbia are, according to Higgins, "Fixtures at Robin Masters' parties." Makes no sense then that they have no idea how Higgins looks like, since it's established that he's been taking care of the estate for over a decade - of course, Masters does not reside in Hawaii himself a lot, but earlier in the episode it is established that he runs those parties at his villa yearly.