In Shakespeare's Hamlet, harmatia, peripeteia, and anagnorisis are present in the play.

Hamartia was seen first in the Greek tragedies. It recognizes the protagonist's tragic flaw; it also states that the character is "missing the mark." Harmartia is described as causing problems where they were not intended or expected. Harmatia is harm...

...committed in ignorance (when the person affected or the results are not what the agent supposed...)

An example of this in Hamlet is found when Hamlet discovers the death of Ophelia. Whereas Hamlet was angry that she seemed to have forgotten him as she worked with Claudius and Polonius to weed out his secrets, he never intended that she would die. When Hamlet sees Ophelia being buried, we understand how much he still cares for Ophelia.

Peripeteia is also from the Greek, describing a "reversal of circumstances" or a turning point in a story. "Peripety" is defined as:

...a sudden turn of events or an unexpected reversal, especially in a literary work, or...

[a] sudden and violent change in circumstances, especially in drama

In Hamlet, I believe this occurs when Hamlet finally gets an incriminating response from Claudius during the "play within a play," when the players put on Hamlet's rewritten drama entitled, Mousetrap. At this point, Claudius is almost certain that Hamlet knows what Claudius has done to become King. Unfortunately, with this knowledge, the villainous Claudius will now try to do away with Hamlet. For example, he sends him to England with the hope that the English will execute him. When that does not work, the King twists the mind of the grieving Laertes and creates a plot that Laertes will act out to kill Hamlet while participating in a sports-based activity of "sword play;" Laertes will use a poisoned sword.

Last, anagnorisis (also from the Greek) refers to a moment when a character discovers an important piece of information.

...is a moment in a play or other work when a character makes a critical discovery... or,

Anagnorisis is the recognition by the tragic hero of some truth about his or her identity or actions that accompanies the reversal of the situation in the plot, the peripeteia. [For example,] Oedipus's realization that he is, in fact, his father's murderer and his mother's lover is an example of anagnorisis.

It can refer to someone's discovery of his own character or insight into the character of another character. It is powerful in that it can bring about a "peripety" that brings about a sudden turn of events.

In Hamlet, we see this in the combined plot development surrounding the Ghost and Claudius, and Hamlet's discovery of what his uncle has done.

At the beginning of Hamlet, the old King's son is approached by the ghost of his dead father who explains that he was murdered by Claudius, his brother. This provides horrifying information not only about the true personality of Claudius, but also the terrible news that Claudius is the murderer of Old Hamlet. This information dramatically shifts the plot (whereas Hamlet starts on a journey to avenge his father's murder), which "galvanizes" the entire plot to its conclusion with the death of all of the remaining principal characters.

Additional Sources:

http://dictionary.reference.com/browse/Peripety

http://www.talktalk.co.uk/reference/dictionaries/difficultwords/

data/d0009849.html

http://www2.hawaii.edu/~zuern/demo/aristotle/terms/

anagnorisis.html