One key area of comedy in this brilliant play is the way that appearances are shown to be opposed to reality. Remember that what start's the play is Marlow's understanding that Mr. Hardcastle's house is actually an inn, with hilarious consequences. Note what he says when he comes to the Hardcastle's mansion:
The usual fate of a large mansion. Having first ruined the master by good house-keeping, it at last comes to levy contributions as an inn.
Yet the theme of appearances vs. reality is something that ironically helps reality emerge. Note how it is Kate's deception and disguise as a barmaid that helps her to discover what Marlow is truly like, and it also helps Marlow relax and be himself with her, eventually deciding to marry her no matter what society will think.
Comedy is also used to explore a more serious theme in the play, which is that of the roles ascribed to particular genders. This play reverses the audience's normal expectations of these, as the audience sees a woman pursuing a man, and not the other way round. This highlights the way that women were seen as financial commodities in that time, as exemplified by the example of Constance, whose value is only based on the colonial jewels she will inherit. By reversing the situation with Kate and Marlow, Goldsmith is indirectly criticising such views that dehumanise women and only see their value as being financial