In Act 1, Scene 5, Hamlet's father's ghost shares how the "whole ear" of Denmark is abused by Claudius who lied about how King Hamlet died. The father's ghost speaks with young Hamlet and directly charges him to hear what he has to say:

Now, Hamlet, hear. 
'tis given out that, sleeping in mine orchard,(40) 
A serpent stung me. So the whole ear of Denmark 
Is by a forged process of my death 
Rankly abused. But know, thou noble youth, 
The serpent that did sting thy father's life 
Now wears his crown.(45) 

King Hamlet's ghost clearly states that Denmark has heard the wrong information. He continues to say that the "whole ear" of Denmark has been "rankly abused" with a lie. As King Hamlet shares what truly happened to him, he orders Hamlet to "hear" the truth. 

In another reference in the story, Act 4, Scene 6, Hamlet writes a letter to Horatio. He has news for him that will make him him "dumb" or speechless:

 I have words to speak in thine ear that will make thee dumb; 

In other words, Hamlet has something to share with Horatio that will leave him speechless. Hamlet gives Horatio orders to come to where he is. Hamlet has a lot on his mind with which to share with Horatio.

The original cause of King Hamlet's death is that Claudius poured poison in his ear. Then Claudius tells all of Denmark a lie. That is why Hamlet's father's ghost states that the "whole ear" of Denmark has been "rankly abused." These are the references to ears and hearing in the play.