One example would be the opening paragraph of this story, which uses a digression to poke fun at the Russian government and its bureaucracy. This is a comic narrative effect because even before the story has started, the narrator pokes gentle fun at the pride and arrogance of members of the Russian internal government:
Quite recently a complaint was received from a justice of the peace, in which he plainly demonstrated that all the imperial institutions were going to the dogs, and that the Czar's sacred name was being taken in vain; and in proof he appended to the complaint a romance in which the justice of the peace is made to appear about once every ten lines, and sometimes in a drunken condition.
The ridiculous nature of this complaint, that sometimes the justice of peace in this "romance" appeared drunk in this novel, highlights the comic nature of this digression, and serves to justify the narrator's choice not to name the department where this story is set in case he receives similar complaints from any Russian official based in the same area.
A second comic narrative effect is when the birth of Akaky is narrated. Having presented him to the reader and his job as being a "perpetual titular councillor," the narrator then describes how he was named in such a way and also ironically pokes fun at this baby through the following quote:
They christened the child, whereat he wept and made a grimace, as though he foresaw that he was to be a titular councillor.
The narrator here refers to the way in which such a title is made fun of by various writers, and therefore links the "grimace" of the child after being named to his preordained fate of becoming a "perpetular titular councillor" and the fun that will be made of him as a result. Gogol therefore uses many comic narrative effects in this short story that serve to engage the reader but also highlight his central theme of injustice to the little man that he explores in this text.