Fish, Abe Vigoda's zodiac sign is Pisces whose symbol is the fish.
Deputy Inspector Luger is forced to take some vacation time and doesn't know what to do with himself so he asks Yemana if Flower Drum Song is still playing on Broadway. Jack Soo, Yemana's actor, was in the original Broadway run and The Movie.
When the squadroom gets a flier for a police department variety show, one of them says "Barney, didn't you sing in college?" and he says no. Hal Linden is a song-and-dance man who's been in many musicals.
Board Game: In 1977 Parker Brothers released a card/ board game featuring the gang at the Ol' One Two.
The Character Died with Him: On January 11, 1979, midway through the show's run, Jack Soo, who portrayed Yemana, passed away. In response, a special memorial episode was aired in which Yemana had been killed. The actors broke character and recalled their favorite Yemana scenes. The episode ended with entire cast raising their coffee cups in tribute.
Inverted with Abe Vigoda as Fish. Vigoda was in his early fifties when the series began, but Fish was implied to be well into his sixties; Vigoda was cast in the role because the producer thought he looked tired during his audition (he had been jogging that morning), which fit the world-weary personality they had in mind for Fish. (Specifically, Danny Arnold looked at Vigoda and said "You look like you have hemorrhoids!")
Yemana claims in one episode that he will be 46 on his next birthday; however, Jack Soo, who played Yemana, was over 60 when the series premiered.
Unwittingly played straight with Steve Landesberg as Dietrich; in his first appearance, Dietrich claims to be 28, and for many years, Landesberg was believed to have been born in 1945, which would have made him 30 years old at the time. However, he was actually born in 1936, making him over a decade older than Dietrich; self-consciousness about starting acting relatively late in life prompted him to lie about his age. (Even at his death in 2010, Landesberg's IMDB page listed his birth year as 1945.)
Jack Soo was a lot of people. A character actor with a long string of credits, you're most likely to remember him in various roles on Mash. He also played Sammy Fong in Flower Drum Song.
Abe Vigoda's best-known role before this was as Sal Tessio in The Godfather.
"Stakeout" from Series 1 features a landlady played by Brett Somers, at the time most known for playing Oscar's ex-wife Blanche on The Odd Couple, but perhaps more well-known now for her long stint as a regular on Match Game. Her husband was Mel Sharpels.
This also applies to people who worked behind the scenes as well. Series writer, producer, and story editor Reinhold Weege later served as creator and executive producer of Night Court, while fellow writer-producer-story editors Frank Dungan and Jeff Stein later served as developers and executive producers of Mr. Belvedere.
The Other Darrin: Abby Dalton played Barney's wife Liz in the pilot, while Barbara Barrie took over the role for the series.
Florence Stanley played Bernice Gruber Fish in seasons 1 and 3. In Bernice's only appearance in season 2, she was played by Doris Belack.
Values Dissonance: In "Blizzard" a man is brought in warning that the blizzard is a sign of a coming new ice age ( in the 70s proponents of climate change talked more of the world cooling rather than warming ). If remade today it seems unlikely he would have been treated as much as a nut as he is here.