Higgins (John Hillerman) tells Magnum (Tom Selleck) that Lady Ashley sent him a "Dear Jonathan" letter, a play on words for a Dear John letter, which is a letter from a woman to a man terminating a personal relationship.
The only other achingly British Lady Penelope known to TV viewers of that generation was Lady Penelope Creighton-Ward, the Bond-esque, ultra-refined marionette character on Thunderbirds (1965). The character's name in this episode is presumably a reference to the other Lady Penelope.
A comment is made about Magnum wearing a sportsoat with jeans. In fact, this was the standard outfit worn by David Letterman when he began hosting Late Night with David Letterman (1982), which debuted the same year as this episode of Magnum.
As seen by the "no outlet" street sign, the King Kamehameha Golf Club is at the end of a private road.