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