During the scene where Castle and Beckett first interview Greg, they say "seriously" a ridiculous number of times. Another throw to Grey's Anatomy, who has been know for excessive use of the word.
The name of one of the doctors at the hospital, Rhonda Chimes, is a friendly poke at/tribute to Shonda Rhimes, the creator of Grey's Anatomy, which is on the same network and is, of course, set at a hospital.
Castle references two Grey's Anatomy characters, McDreamy and McSteamy.
The short female doctor with a forearm crutch is a nod to Dr. Kerry Weaver character played by Laura Innes in TV-series medical drama "ER".
This episode is named after the movie, "Anatomy of a Murder," which is about a murder case that takes place in the upper peninsula of Michigan.