The name of J.D.'s "mirror image", Mrs. Zeebee, is an obvious reference to actor Zach Braff's initials, ZB.
In this episode, the patient to whom Dr. Cox relates (for their mutual anger management issues) is named Mr. Slydell. John C. McGinley (who plays the part of Dr. Cox) plays a character by the name of Bob Slydell in the movie Office Space (1999).
The name of the Janitor's mirror image, Mr. O'Neil, is a reference to Janitor actor Neil Flynn's first name.
The Janitor's mirror image says he spent most of his life trying to become a lawyer but could never get his Jurist Doctorate - he "spent years trying to get that damned JD" (i.e. the Janitor has spent years trying to get JD).