The amphibious aircraft from Chalk's Ocean Airways, seen in the end of the episode with registration N2969, first flew in 1947. It crashed on December 19, 2005 (Flight 101 from Miami to Bimini), killing everyone aboard - 2 crew and 18 passengers. The right wing separated in flight shortly after takeoff because of existing cracks due to metal fatigue that had been improperly repaired by the maintenance crew. The same plane was featured at the end of the Miami Vice pilot.
Michael Des Barres was the lead singer for Power Station, and previously appeared as himself in this role in Whatever Works (1985), which featured the band performing live in a bar that Crockett and Tubbs visit. Des Barres was married to Pamela Des Barres from 1977 to 1991, who once was also reportedly romantically involved with Don Johnson.
The stunt with the speedboat jumping the tug and grounding on the island must be one of the most spectacular ones in all five seasons of the series, particularly since it all had to be done practically in a time before CGI.
The plot, involving a foreign diplomat using their immunity from prosecution to engage in illegal dealing, is very similar to that of Lethal Weapon 2 (1989), which came out the following year. In the film, the antagonists are dealing in drugs rather than weapons.
Chile, like many other South American countries, was led by a dictator at the time, General Augusto Pinochet, who ruled from 1973-1990. Ernesto Guerrero was an official in Pinochet's government. Crockett mentions to Guerrero "Down there in Chile, this may give you a license to kill, here in Miami, it don't mean squat!", which is a Reference to Pinochet's Dictatorship.