The character name "Dwayne Reed" is a pun on "Duane Reade," the ubiquitous New York drug store chain, while "Carol Anne Keane" plays on "Carolyn Keene," the nom de plume of the various authors who wrote the Nancy Drew mystery books.
The premise has many similarities to the Michael Peterson murder case. Peterson was a novelist in North Carolina and the character Larry Henderson is a poet in South Carolina. They are both accused of killing two wives in the same fashion (Peterson by pushing both down staircases and Henderson through windows) and both the real and fictional cases involve birds as a defense.
Anne's known disorders so far are prosoapamnesia, dyslexia, involuntary emotional expression disorder, stendhal syndrome, foreign accent syndrome, nocturnal lagophthalmos, a form of dystonia called 'backwards cheerleader syndrome', and a condition where her left hand does what it wants.
This series premiered exactly 20 years after the film of the same name. Although the film is unrelated, it did star Michael Richards who was a huge star on NBC at the time (Seinefld). NBC is the network that airs Trial and Error.
The characters in the show regularly break the "Fourth Wall"; by looking directly into the Camera, whether they are explaining a scenes, backstory or simply looking at the camera - ergo the audience - to extend the humour in a scene.
Larry states he has a twin brother named Harry, a few episodes later French Stewart plays witness coach Sebastian Rappaport who coaches Larry for the stand. French Stewart and John Lithgow starred together in their long running tv show '3rd Rock from the Sun' ironically Stewart played Lithgow's brother Harry. It's well know that the entire '3rd Rock' cast has remained incredibly close even after the show's ending.
The trivia item below may give away important plot points.
While coming up with alternate theories in the pilot, Josh tells Dwayne and Anne to say the first thing that pops into their head, Dwayne says "Bird. Birds fly into windows all the time." In the finale it is revealed Margaret was in fact killed by an owl.