This does not speak well of Soviet satires, and I would like to leave a flaming bag of poo on the doorstep of 'some critics'.
This came up as a selection in the Resistance Book Club, but sadly there is more meat for discussion in Bulgakov's Wikipedia page than the novel. The censorship he faced in life, and the fact that the novel circulated in samizdat and was only published years after the author's death, have much more to do with authoritarianism than the book itself.
To be sure, one element of the book is that a novel about Pontius Pilate is suppressed by the Soviet literary establishment for being too religious, but that's about an end of the criticism of the Soviet state (per se) other than some small-time humor about bribes, cliques and the chicanery required to land a decent apartment in Moscow.
Bits of the Pilate novel are also interpolated into The Master and Margarita, and are in fact the best written parts of it, since the remainder is a mostly tedious slapstick farce of Satan and his minions visiting Moscow and wreaking havoc. The historical scenes are a serious and sympathetic literary take on Pilate, grounded in the gospel narrative, but adding to it dramatically.
A highpoint of the modern era story is a Satanic Ball, because who can argue with that?
It's possible I chose a poor translation. Well, no, it's not possible, it's certain. I'm just not very sure that my opinion would have risen much with a better translation. I'm gonna pull my Hipness Through Erudition card, and note that when Pontius Pilate is described as a 'rider', what was meant was that he was of an equestrian family.
Favorite 'joke': one of the demons takes the form of a huge black tomcat, walking about on his hindlegs. He gets on a Moscow streetcar. The other locals might not have objected to this so much, had he not attempted to pay for his passage. Rimsky-shot.