Avoiding Responsibility
The two main characters of the novel demonstrate a certain juvenile desire to flee from their problems. For Peter, it's his arrest warrant back home. For Kit, it's her undesired marriage proposal from Sir Phillip Morton. Neither of the two can really be blamed for not wanting to address these problems directly, but they do take things to the extreme. They both, separately, run away to join a theater troupe and travel the countryside. They aren't interested in making restitution or putting a stop to their anxieties, preferring instead to pretend they no longer exist because they cannot be directly seen in this new environment.
Suspicion
If ever someone was uniquely position to suspect a conspiracy, it's Peter. He stumbles upon an elaborate assassination plot in which he's apparently wrapped because of his beef with Sir Phillip. Sir Phillip has entrenched himself in a sophisticated band of criminals who are determined to make themselves wealthy at the expense of the rest of the country. As Peter starts noticing more and more strange circumstances occur while he's with the actors, he begins to put some pieces together. He becomes paranoid that someone is out to kill him. Then he thinks maybe Kit is the target. When he finally has enough confirmation of his suspicions to begin to understand the actual consequences of Sir Phillip's scheme, Peter almost feels relieved. He's harbored so many suspicions for so long that he's severely questioning himself by the time he realizes that he's figured out the actual threat. He really can't be blamed for distrusting everybody at this point and taking it upon himself to be the one to end these wrongdoings.
Reputation
Reputation plays a significant role in a such a small, rural community as Peter was born into. Cumberland is just a village still. When Peter insults Sir Phillip by throwing stones at him, he's cost his elder greatly. Nobody in the village will ever forget that Sir Phillip got bested by a boy the way Peter did. Naturally this leads Sir Phillip to desperately attempt to restore his reputation by consequently defaming Peter. He needs this boy to be humiliated, in a manner just as intense as the way Peter embarrassed him. Of course, Sir Phillip is not a prudent nor especially kind man, so he takes it upon himself to ruin Peter's life. This is why he goes tot he authorities and demands a warrant for the boy's arrest. All of this is a vain attempt to undo the insult already paid. In the end, Peter is really the one to learn about the power of reputation as he realizes that everybody who knows him is now willing to get him arrested. He has to leave because he insulted the wrong guy.