The trailer even plays up the comedy in the film.
But make no mistake, the film is a major introduction to the horrors committed in the Soviet Union under the regime of Joseph Stalin and the plotting that followed his death.
Raphael Abraham, writing for Financial Times, captures the film perfectly "As this coven of vampiric apparatchiks feasts on the remains of Stalinism, the unremitting blackness of the situation at times threatens a full comedy eclipse. But the discomfiting balancing act of humour and horror is precisely Iannucci's game—and only he could pull it off with such skill."
It is no wonder that the socialists choke when watching this film.
David Walsh, writing at the World Socialist Web Site, says the film, "Taken in and of themselves, there are amusing lines and moments, until one remembers the general context and the historical stakes, and the laughter freezes in one’s throat. All the actors are fine at doing what they are asked to do, but what they are asked to do is terribly off the mark. It is impossible to make sense of a film like The Death of Stalin except in the context of the terribly low level of historical knowledge or interest that exists in the arts at present."
As for the historical accuracy. It's not bad allowing for dramatic license.
A number of academics commented on the historical accuracy of The Death of Stalin. Historian Richard Overy noted in The Guardian that the film "is littered with historical errors", which can be "viewed as cinematic licence" but was most critical that the film did not appropriately honor those who died during Stalin's leadership. Director Iannucci stated that he "chose to tone down real-life absurdity" to make the work more believable.
Samuel Goff, at the Department of Slavonic Studies, University of Cambridge, while admitting that the film′s historical discrepancies could be justified inasmuch as they helped focus the drama, found turning Beria into "an avatar of the obscenities of the Stalinist state" misses the chance to say "anything about the actual mechanisms of power".Goff believed that Iannucci's approach to satire was not transferable to something like Stalinism, and the film is "fundamentally ill-equipped to locate the comedy inherent to Stalinism, missing marks it doesn't know it should be aiming for"
But forget these criticisms, the general theme and history are correct which most importantly reminds us of the horrors of Stalin's Soviet Union.