Critics still disagree to some extent over the quality of Gogol's Ukrainian tales and the extent to which they reflect the artistic vision found in his later, most famous pieces. I would acknowledge that there aren't any absolute masterpieces among these stories, but the world he creates through the lot of them, with the constant presence of the supernatural (probably best seen in "The Night Before Christmas" and "Viy") and a charming provincial sense of humor (at its height in "The Story of How Ivan Ivanovich Quarreled with Ivan Nikiforovich"), is really quite memorable. Also, it's very interesting to see how the simple country folk of the Ukrainian tales evolve into the often equally naive clerks found in the Petersburg tales, and how the demons and ghosts of Gogol's earlier pieces anticipate the haunted portraits and phantoms of departed eternal titular councillors that would later win Gogol lasting fame.
It is, however, the Petersburg tales that are really the centerpiece of the collection. Though it would be a mistake (one that has tempted many a socially-minded critic over the years) to portray these stories as representing a profound sympathy on Gogol's part for plight of the little man, Gogol uses humble copying clerks, struggling artists, and their ilk to paint a wondrously alive picture of the bustling imperial capital. In each of the stories (among which I should mention "Nevsky Prospect" and "The Portrait," neither of which appears in anthologies nearly as often as it should), Gogol infuses the experiences of a seemingly undistinguished individual with something extraordinary, sometimes using the supernatural and other times exploring the protagonist's dreams or his madness. Though Gogol's contemporaries (like Pushkin and Lermontov) were producing a number of excellent works at the same time, those works tended to focus more heavily on the privileged few, and, innovative though they were in various ways, they were written somewhat more in the spirit of the works of foreign authors like Byron and Scott. In Gogol's Petersburg Tales we see Russian masterpieces written for almost the first time in a relatively non-Western European style about the masses who were not lucky enough to belong to the high nobility, and these works (though Gogol surely had no intention of things turning out this way) would go far to influence the social realism developed by later Russian authors.
Gogol's prose is known among Russians for its beautiful lyricism, which sometimes fails to come through in translation. This translation is (unsurprisingly, given how widely praised Pevear and Volokhonsky are) an exception to that; each of the four stories in the volume that I had previously read in other translations improved substantially under the influence of Pevear and Volokhonsky, and throughout the volume I often marvelled at the elegance of the narrative. The one complaint I might have about the collection is the omission of the historical romance Taras Bulba, which is probably the best known of Gogol's Ukrainian tales and is substantively different from any other story he wrote. However, since (at about 120 pages) it might better be described as a novella that a short story, and since the volume is already slightly Ukraine-heavy, it's understandable that Tara Bulba didn't make it in. Other than that issue, I can't think of a single weakness in the collection, and I highly recommend it to anyone with any interest in Russian literature or in the development of the short story as an art form.
As to the stories themselves, the best of them (the Petersburg stories, that is) must rank among the greatest of all works of short fiction. "Diary of a Madman" is one of the most convincing and frightening of all fictional representations of madness, made all the more so by its abundance of comic detail. "The Nose" is a surreal satire which must be read to be believed, and "The Overcoat", with its combination of linguistic dexterity, close character study, and a narrative that veers between the moralistic and the ambiguous, is a concoction unique in literature. I also wish to put in a good word for "Nevsky Prospect", the two-headed tale of the differing fates of a self-satisfied philistine and a romantic dreamer, both of whom succumb to forces of deception.
Realist, anti-realist, surrealist--take you pick, Gogol is any and all of these, and one strand doesn't invalidate any of the others. You can take the Petersburg stories as a swipe at Russian bureaucratic tyranny; or as a study of malign spiritual and psychic forces; or as wacky entertainment. As with any genius, his works suggest multiple points of departure.