That Chekhov wrote this remarkable novel at the age of 24 is almost as impressive as Thomas Mann's writing of "Buddenbrooks" at the age of 26. "The Shooting Party" has a greater sense of feverish, almost Dostoyevskian intensity compared with Chekhov's later work, perhaps attributable to his youth. But it also has the same deep human understanding and descriptive ability - in Chekhov's almost minimalist style - as the later stories and plays.
The structure of the story-within-a-story and the metamorphosis from provincial novel of manners to an account of sexual misconduct and moral turpitude (in 19th century terms) to detective story, all within the space of a 200 pages, may seem a little clumsy to a modern reader (and the identity of the murderer may also be a little more obvious now than it was to a contemporary reader), but achieving all of this in such a short novel takes a great deal of talent, and Chekov's great talent is apparent even at this early stage of his career. It is also a fascinating and compelling novel, both for its account of provincial Russian life, as well as the psychological portrayals of the characters and the "whodunnit" element.
The previous review appears to refer to the 1926 translation (by Constance Garnett?), which no longer appears to be in print. This review relates to the new Ronald Wilks translation, which is adequate, though not outstanding. Constance Garnett's translations of Chekhov (which are still widely available) tend to be very readable and idiomatic (in English), if not always faithful to the original. Like many modern translations of Russian, this translation is occasionally a little wooden, and uses expressions or words that would generally not be used in English, reinforcing the fact that it is a translation. Not being fluent in Russian, I can't comment on its literal accuracy. However, despite these flaws, the translation conveys the story and the meaning of the text perfectly well.
One area for criticism - as is often the case in Penguin classics - is that the notes are often intrusive (and occasionally unnecessary, although not nearly so bad as in other books), and I personally object to the appearance of footnotes within the text. I also object to the introduction - which gives far too much of the plot away - appearing at the beginning of the book, especially as so many readers insist on reading the introduction first. Personally, I would prefer to see critical comments appearing after the text of the novel.