Bleeding like a Russian princess is a reference to the prevalence of hemophilia in the royal bloodline.
The episode won an Emmy Award for Outstanding Animated Program.
Cyril tells the other agents that one of them can put a different name on the agency after they have 2,000 hours of private investigation work during the next year that he approves. To become a PI, the actual requirement in California for someone without a law degree or criminal justice background is 6,000 hours over three years with approval of a licensed agency. Cyril might just be letting them find out slowly.
In the opening, a dead body is floating in the swimming pool of a Hollywood mansion belonging to a "has-been" actress. This is a reference to Sunset Boulevard (1950), in which the body of Joe Gillis (played by William Holden) is found dead in the pool of aging screen legend Norma Desmond (played by Gloria Swanson).
Ray makes a reference to TC in the chopper. This is a reference to Magnum, P.I. (1980), the show spoofed in the advertising campaign.