In what ways does Hamlet appear to change during Act Four?
Act Four opens immediately after Hamlet has killed Polonius and dragged away his body. This is the first instance of significant violence that Hamlet has actually acted upon rather than merely thought about. Gertrude comments that Hamlet is as "[m]ad as the seas and wind, when both contend / Which is the mightier," and, indeed, Hamlet seems to have gotten even crazier than he was in the previous three Acts. Hamlet continues to behave like a person who has come unhinged, messing with the minds of Rosencrantz and Guildenstern, hiding Polonius' body, and antagonizing Claudius and the court.
Act Four, Scene Four also contains an important soliloquy in which Hamlet considers his lack of action over the murder of his father in comparison to the war being waged over something as meaningless as a small plot of land. He tells himself to have his "thoughts be bloody, or be nothing worth," which marks a renewed commitment to his plans for revenge. Overall, Act Four seems to suggest that Hamlet is now erratic enough to commit the murder he's so fervently been contemplating over the course of the play.
Hamlet becomes increasingly erratic in his behavior. This causes quite a bit of questioning on Hamlet's sanity. His lack of avenging his father's death has turned into despair. His reluctance to act is lessening by the end of act IV, and in act v he will be ready, at last.