Charles as the studier of - and victim of - evolution (Situational Irony)
Charles is a paleontologist; that is, he studies fossils and tries to determine information about the flora and fauna of previous eras of our planet's history. Evolution is a key part of paleontology, because it is by examining fossils that we develop ideas about how species have changed over time. Charles views himself as a man of progress, a forward-thinking intellectual in contrast to, for example, Ernestina's father, who does not believe in Darwin's theories.
The irony is that Charles himself is a victim of a type of social evolution: his social class is on the brink of being overtaken by the lower classes, who are 'more fit to survive', and his fellow independently wealthy, aristocratic London gadabouts will soon become relics of the past. When Ernestina's father offers to make him a partner in the family business, Charles cannot accept, because he doesn't think that it is fitting for a gentleman to go into commerce - he is unable to adapt to a changing environment, and so he is a "victim of evolution" (228).
Sarah's reputation for sexual immorality (Dramatic Irony)
This is a clear example of irony. Sarah is seen as sexually immoral by the whole of Lyme Regis, and her reputation is ruined because of what everyone believes to be true about her illicit 'affair' with the French lieutenant. People refer to her as a 'whore', and she inspires scorn in many, and pity in some - premarital sex is viewed as unacceptable in the society in which she lives.
This is painfully ironic, of course, because Sarah is not sexually immoral, and is actually a virgin for the majority of the novel. Most people try to cover up nasty secrets about themselves in order to avoid a bad reputation, and Sarah deliberately courts scandal by contributing to the creation of a false story about herself.
The upper-class view of their 'immoral' servants (Dramatic Irony)
In Chapter 14, Mrs. Poulteney and Ernestina discuss the behavior of Mary, Mrs. Tranter's maid, and Sam, Charles' manservant. The old woman and the young lady agree that the domestic servants need to be spoken to about their unacceptable flirtatious interactions, which aren't "proper" in the context of Lyme Regis (88). They focus in particular on an incident earlier that morning when Mary was seen "talking with a person...A young person" (88). The implication is that this encounter was improper in some way, probably because it had sexual undertones (Ernestina comments that Mary "is too easily led") (80).
We learn at the end of the scene that the encounter in Mrs. Tranter's kitchen between Mary and Sam was "surprisingly serious" and that they barely made eye contact, and when they did, it was "shyly" (89). It is ironic that the upper classes are condemning their servants for imagined misdemeanors when the interactions between them are actually very innocent, and as restrained as would be deemed acceptable for young ladies meeting their aristocratic suitors in high society.
Charles, the thwarted inheritor (Dramatic Irony)
In Chapter 23, Charles finally leaves Lyme Regis and goes back to where he grew up. Charles hasn't lived there for a while; he flitted about during his college years, preferring to travel than to settle down in the country mansion and learn how to run the estate. In this chapter, however, we see a shift in his attitude - he feels a "call to the throne" and is ready to take on the duty of inheriting and managing the house and land (158).
The irony here is that now that Charles finally feels the urge - and a strong urge, too - to take up his position as lord of the estate, his uncle is going to deny the fulfillment of this wish. Charles was certain that Uncle Robert would offer him the great house to move into with Ernestina, but Uncle Robert has other plans: he is going to remarry and keep the house for himself.