In a conversation with Anona, Auntie Hilo refers to "haole" missionaries. "Haole" is a Hawaiian term for nonnatives, particularly Caucasians.
Lots of background stock footage shots of mid-century Honolulu. During the scene at the bird shop, the original International Market Place looks like the backdrop. And there's an evening panorama of Waikiki with the original Pink Palace (Royal Hawaiian) and Moana hotels, as Paul reports back to Perry on his progress.
Santo and Johnny (with band) are playing in the nightclub scene with dancers at about 13:00. Santo is playing the steel guitar and Johnny the electric guitar on the far right. The bass and ukulele players are unknown. Santo and Johnny are famous for their 1959 instrumental "Sleep Walk" which was a huge hit and has since been covered by dozens of other artists.
This is one of only two cases in the series where Perry practices law outside of California. In The Case of the Fugitive Fraulein (1965) he defended a client for murder in East Germany, after going through the hoops to get permission from the East German government. It's unclear in this case whether Perry is licensed to practice law in Hawaii (he was there to scope out a land deal) or received special permission from the court to defend Anona (a process called pro hac vice). In another case, The Case of the Shapely Shadow (1962), Perry was prohibited from even talking to his client when she was arrested in Las Vegas because he wasn't licensed to practice law in Nevada.