Carrying Things as a Priviledge
Prince Brat is excited to carry the jugs of milk because he has never been allowed to carry or fetch anything before. This is ironic because to people who are not royal and who therefore have to carry and fetch all the time this is not a priviledge at all but a chore they would gladly give up.
The Illiterate Prince and the Literate Whipping Boy
Prince Brat is a privileged boy who does not even have to attend a common or garden school but has a private tutor. However, because he does not value this educational opportunity he doesn't pay attention and cannot yet read or write. Jemmy is the hitherto uneducated son of a rat catcher and has never attended school but because he values education he pays attention during Prince Brat's lessons and has learned how to read and write.
Outlaws Flee To An Island
The outlaws are last seen fleeing the tunnels of the city and the rats there and running away to an island but ironically the island turns out to be a prison colony so they have escaped freedom and headed to a penal colony without anyone having to bother to capture them.
Soldiers Staring At Prince Brat
At the fair Jemmy and Prince Brat are very nervous because the place is swarming with soldiers sent by the king to look for them. At one point the soldier whom they pass by starred directly into Prince Brat's face. The irony is that they cannot recognize his face and have known him only by his overall appearance so that now he is in rags and not in his Royal finery they do not recognize him even when looking right at him.
Prince Brat Wants Friends
Prince Brat is so nicknamed because he is utterly obnoxious to be around and is mean to everyone. He even expects Hemmy to want to be his friend to order. The irony here is that he cannot see that his bratty behavior is driving people away and that by trying to bully them into being friends with him he is actually creating the opposite outcome from the one he is wanting.