In Act four, the ramifications of Polonius's death (performed in Act three Scene four) ultimately put in motion the destruction of every major character except for Horatio. Claudius decides to send Hamlet to England and have the King of England kill him. Because Hamlet discovers the warrant for his own death—as he relates in Act five Scene two—he has Rosencrantz and Guildenstern murdered instead, decides for sure to murder Claudius, and arranges to go back home for that purpose. Meanwhile, Laertes's rage at the murder of his father, and the way it has driven Ophelia mad, makes him ready to kill. Claudius persuades him to attack Hamlet rather than Claudius, leading to the fatal duel and the deaths of both Hamlet and Laertes. In Act five, Claudius's fail-safe measure, the poisoned pearl, claims the life of his queen. Laertes reveals the plot, leading to the murder of Claudius. None of this would have happened without Claudius's and Hamlet's actions in Act four in response to Polonius's death in Act three.

To argue this is basically to argue that the events at the end of Act Three constitute the climax of the play. In Act Three, Hamlet ascertains (through the King's reaction to the play) that Claudius is responsible for his father's murder. He still fails to kill him, but after confronting his mother, he accidentally kills Polonius. This is one possible climax of the play, because afterwards Hamlet and Claudius (and for that matter Laertes) are on a collision course with each other. One or both of them will be destroyed, regardless of what else happens. The events of Act Four and even Act Five—Ophelia's madness and death, the King's failed plots to have Hamlet executed by the King of England, and then killed by Laertes—simply build toward the fateful final scene. There Hamlet gets his revenge, but only at the cost of his own life. There is, in a sense, a straight line from the death of Polonius to the deaths of Hamlet, his mother, Claudius, and Laertes in the final scene. Of course, there are many contingent events in these scenes, most notably Hamlet's contrivance to escape his fate in England, and the duel scene itself. But it could certainly be argued that Acts Four and Five witness the falling action of the play.

After his killing of Polonius at the end of Act III, Hamlet is no longer a hero in the conventional dramatic sense. So long as he was planning to avenge the murder of his father, all was well and we were very much on his side. But after having dispatched poor old Polonius, it's difficult for us to feel that Hamlet enjoys much in the way of moral superiority over Claudius. Polonius's murder may well have been accidental, but Hamlet shows no contrition whatsoever in depriving Ophelia and Laertes of a father just as Claudius deprived Hamlet of his.

One could say that the action does indeed break down in Act IV in that the focus of the play becomes more firmly fixed on Hamlet's increasingly tumultuous mental state than on his desire to wreak revenge. There is still plenty of action to be sure but much of it appears divorced from Hamlet's initial plan of action. The exploration of character becomes ever more important than action in Act IV. It is this feature more than any other that gives it something of a lopsided feel.

Ah, good question. You could see the action of the play as breaking down after Act III because it changes in nature. The first three acts are tightly focused, and tension is building. After that, though—and I'd marked the turning point at the place when Hamlet kills Polonius—the focus of the play seems to shift. Earlier on, Hamlet was testing the ghost's message, seeking evidence of guilt, and trying to kill Claudius. After that, we've got Hamlet sent away, Ophelia going crazy, the graveyard scene, etc. Even the simple fact that there are seven scenes to Act IV shows a kind of structural imbalance.