The title is a pun based on the phrase "Embarrassment of riches," which means "too much of a good thing," and on the fact that female dogs are referred to as "bitches."
Nana Visitor plays a pet therapist in this episode. Michael Dorn, who starred with Visitor in Star Trek: Deep Space Nine, plays Beckett's therapist in this same season.
Nathan Fillion and Justin Hartley have both played DC Comics superheroes. Fillion has played Hal Jordan/Green Lantern in four animated straight-to-DVD movies, and on Smallville (2001), Hartley was the first actor to play a live-action version of the Green Arrow.
Hilarie Burton Morgan, who plays Kay Cappuccio, has a cat called 'Poe' who's named after writer Edgar Allan Poe. Richard Castle chose his second/middle name, 'Edgar' after said writer.