Both Diane Venora and Liev Schreiber have previously acted in productions of 'Hamlet' on the New York stage. In fact, Venora had actually played the title character in a famous and iconoclastic production of the play.
Ophelia removes a rubber duck from her bag. This is a reference to Aki Kaurismäki's version of Hamlet, Hamlet Goes Business (1987), where after the death of his father, Hamlet's uncle controls the board of a company that decides to move into the rubber duck market.
In the scene in which Claudius confronts Hamlet in the laundromat, he pushes Hamlet from machine 2 to machine 3. This correlates with Shakespeare's play, in which the confrontation begins in Act IV, scene 2 and continues on to scene 3.
In keeping with the modernized presence of all things Shakespeare throughout the film, Hamlet travels on a plane. This is also a play on words because in the original text of the play the scene takes place in "A plain in Denmark".
When Hamlet stops the limo after deciding not to kill his uncle, Claudius, he exits at a theater billing the Best Musical of 1998 - the live-action stage version of "The Lion King". "The Lion King" is reportedly inspired by "Hamlet".
William Shakespeare was both a playwright and an actor, and is widely believed to have played the ghost of Hamlet's father in early productions. In this film, the Ghost is played by Sam Shepard, who is also both an actor and a playwright.
When Hamlet is in Blockbusters, saying his soliloquy, the film that is playing is The Crow: City of Angels (1996), the second installment of the Crow series; a series in which the protagonists are sent to avenge the dead and set things right.