What are the reasons for considering the murder of Polonius as the turning point in the play Hamlet?
You are right in identifying that Hamlet's murder of Polonius is a very significant turning point in the play. Firstly, let us remember that this is Hamlet's first act of open violence in killing somebody. Following "The Mousetrap," now Claudius understands the true danger that Hamlet represents to his person. Note what he comments to Gertrude in Act IV scene 1:
His liberty is full of threats to all,
To you yourself, to us, to every one.
Claudius realises the way that Hamlet's presence threatens his own life and power, and continues to act to do away with him, and thus the murder of Polonius represents an escalation in the conflict between these two characters.
In addition, this scene is important because of the way in which Hamlet confronts his mother after killing Polonius, and makes her see the impropriety of her actions and doubt her husband. This represents the first break in the relationship between Claudius and Gertrude, who up to this point in the play had been united in purpose. Gertrude in Act III scene 4 agrees not to sleep with Claudius any more and obviously begins to side with Hamlet.
Lastly, let us remember how the murder of Polonius impacts Ophelia and Hamlet's relationship with her. The madness of Ophelia as demonstrated in Act IV scene 5 and the way that her father's death at the hand of her lover has made her "importunate" and "distracted" is of course key in the way that Laertes comes to side with Claudius against Hamlet, leading to the final tragic duel that kills them both.