Archie Miles' name is a play on the name of Miles Archer, Sam Spade's partner in The Maltese Falcon (1941).
This was the first appearance of private investigator Harry McGraw, as played by Jerry Orbach. Of all of the recurring characters that helped Jessica, the McGraw character is the only one spun off into his own series.
Jerry Orbach and Angela Lansbury would later star together in Beauty and the Beast (1991) as Lumiere and Mrs. Potts, respectively.
At one point, Jessica mentions a Senate election to be held in the following year. Since neither of Massachusetts' two Senate seats was being contested in 1986, it is likely that the producers deliberately put the fictional Senate race in that year.
Just before the detective gets murdered there is a copy of the Maltese Falcon, from the film of the same name, in the background.