There are three possible turning points in Hamlet: the players's cene when Claudius' guilt concerning the murder of King Hamlet is confirmed; the prayer scene when Hamlet forgoes the opportunity to kill Claudius; and the closet scene where Hamlet first takes action, but kills Polonius inadvertently. In the players's cene, the ghost's story is proved to be true, allowing Hamlet to avenge his father's murder. In the prayer scene, Hamlet misses a perfect opportunity to kill Claudius, giving Claudius time to act against Hamlet. In the closet scene, Hamlet's actions give Claudius the impression that he poses as a major threat to his continued succession on the throne.
The death of Polonius also triggers a series of repercussions by altering the characters' mindsets. In the players's cene, Hamlet revises the play of The Murder of Gonzalo, adding in a scene that hints at the murder of King Hamlet. When Claudius reacts to Hamlet's trap and makes a sudden exit, Hamlet now knows that the ghost's story is true and will "take the ghost's word for a thousand pound." He now has no reason not to act. Prior to witnessing Claudius' reaction, Hamlet has been debating with himself over the legitimacy of the ghost and its story. He has been questioning himself and whether he is a coward, because all he has done is talk, not having taken any action.
Now that Hamlet knows the murderous sin Claudius has committed, Hamlet feels no guilt in avenging his father's death. The plot takes a turn, as Hamlet becomes more of a man of action than a philosopher. In the prayer scene, Hamlet misses his best opportunity to kill Claudius and avenge his father's death. With no guards around, Claudius is alone and he is unaware that Hamlet is lurking in the shadows. The scene is set for Hamlet to take vengeance for his father's unsettled spirit. However, Hamlet does not kill him, because Claudius is repenting for his sins, allowing him to go to heaven when he is to die.
As one's religion often dictated the afterlife of one's soul, King Hamlet is doomed to an eternity in purgatory. Hamlet does not feel it is fair for Claudius to go to heaven, while his father is at unrest, so he decides instead to kill Claudius while he is doing something sinful. This is ironic because Claudius says he is not really praying; he is just going through the actions of prayer. He doesn't want to give up all that he has gained, such as the throne and his wife, Gertrude. Therefore, Hamlet really did miss a perfect opportunity to kill Claudius, because Claudius would not have gone to heaven after all. This scene shows Hamlet's indecisiveness, because after the players's cene, he vows to take action in murdering Claudius.
However, when the opportunity rises, Hamlet doesn't take it. One might think that Hamlet is just making up excuses to avoid murdering Claudius. In forgoing this opportunity to kill Claudius, Hamlet allows Claudius time to act against him. Claudius attempts to rid himself of Hamlet and the possibility of his crime becoming discovered.
In the closet scene, Hamlet kills Polonius, thinking it is Claudius behind the curtain. When Hamlet goes to his mother to talk, Polonius is hiding behind the curtain and eavesdropping on their conversation. Polonius wants to prove that Hamlet's behavior is based on Ophelia's rejection of Hamlet's love. Hamlet hears him behind the curtain and stabs him, thinking he is Claudius. This is an important turning point in the play, because this is the first time that Hamlet has taken action towards avenging his father's death. Even though he has killed the wrong person, he has finally done something other than philosophize about retribution and murder.
This scene also shows how Hamlet has changed as a character. Logically, it isn't possible that it is Claudius behind the curtain, because Hamlet has just seen Claudius repenting for his sins and praying in another room. If Hamlet had taken the time to think things through, rather than automatically thinking it is Claudius who is spying on him, he would not have made the mistake of killing Polonius. In the beginning of the play, Hamlet is someone who deeply thinks things through, but this scene shows how he has changed into a more impulsive character who doesn't think enough before acting. The closet scene is the most logical turning point. It shows Hamlet as an impulsive man of action, rather than an indecisive thinker.
It is the first time Hamlet has taken action against Claudius. Before this scene, Hamlet has only made indirect pointed remarks against him. The closet scene is the biggest turning point in Hamlet because there is a great series of repercussions following the death of Polonius. Claudius becomes increasingly nervous after Polonius' death, because he knows that Hamlet was meaning to kill him rather than Polonius. Pending that fear, Claudius arranges to have letters addressed to England to kill Hamlet. Also, Ophelia goes mad because of her father's murder, and consequently ends up drowning to her death.
Laertes also comes back to Denmark from France to seek revenge for his father's murder. It is arguable that had Hamlet not murdered Polonius, none of these events would have occurred, including the deaths of virtually all the characters as well as Hamlet. The three main turning points of Hamlet all revolve around Hamlet seeking revenge for his father's murder. The three scenes depict Hamlet's growth of character from a hesitant philosopher to a rash man of action. In the players's cene, Hamlet takes extra care in confirming the authenticity of the ghost's story, while deeply debating the morality of killing Claudius. In the prayer scene, Hamlet remains indefinite in the decision of taking vengeance for his father, as he neglects his best opportunity to end Claudius' life.
Hamlet makes a drastic change of character in the closet scene when he kills who he thinks is Claudius without hesitation. This shows he is now ready to take action for his father. However, it is Polonius behind the curtain, and his death sets off a chain of unexpected events that alters the plot and characters of Hamlet.