Order is restored at the end of the play in a very obvious and very limited sense (imagine how different the ending would be if Fortinbras had not been nearby!), but the most powerful emotions felt at the end of the play are such emotions as sadness, disgust, terror, pity, and a profound sense of waste and loss. Fortinbras is not characterized very fully earlier in the play; his fortuitous appearance almost has a touch of the "deus ex machina" (god out of the machine) about it, as if Shakespeare wanted to get an already long tragedy over with and not spend much time speculating about the future of Denmark.
I think #3 makes an excellent point. Let us not forget the way that the death of a monarch or a ruler has such catastrophic consequences to societies in some of Shakespeare's other plays, such as Julius Caesar and Macbeth. Whilst we know Fortinbrass receives the crown at the end, it is very clear that the future of Denmark is unclear, as he will have to bring stability and peace to a realm that has suffered so much from the end of Hamlet's family dynasty.
There is no order except through fighting, and there is no restoration. Fortinbras is in Denmark as an enemy of the state. He may create a less chaotic country, but based on how he took the throne he is likely to maintain it only through martial law. No one can see restoration in this disastrous ending except for Fortinbras. He believes King Hamlet took what was not his from Fortinbras' father, and it is now being restored to him.
I agree with post 3. There is nothing orderly at the end. It is death and utter chaos. There will have to be a whole new beginning because no one in the family is left standing. It is absolutely incredible to think of how many people died at one time. There is no way to restore the deaths of Gertrude, Claudius, Laertes and young Hamlet. No doubt, Fortinbras stood in utter shock at the people lying dead.
I don't think it is fair to say that "order is restored at the end." A whole dynasty is killed off. A new order of royalty will have to be established. An entire new rule will descend upon the unwitting people of Denmark. Fortinbras of Norway establishes a new order for the country of Denmark: nothing is restored.
I think the fact that this time period of time operated so heavily on the divine right of kings that the entire country would feel in some way involved in the family feud. However, we look at the known characters left alive and consider the question for each.
Fortinbras takes over the throne with praise for Hamlet. He intends to rule, and every indication is that he will be successful. He has undertaken his plan to regain family claims perfectly and has avoided bloodshed completely. Because personal flaw has caused the downfall of Hamlet and his family, Fortinbras can avoid the curse.
Horatio tearfully bids his friend Hamlet goodbye after warning him of his impending doom and attempting to kill himself. However, after being charged with telling Hamlet's tale, he lives to uphold this duty. He has been the epitome of the true friend, and, other than feeling grief, Horatio does not seem to be in line for any additional misery.
Basically, Fortinbras must be viewed as capable of ruling and preserving Denmark for Horatio and the other minor characters.