Alamo Drafthouse finally opened in Raleigh (they're doing staff training days, and you get 50% off your food order) and I saw it the other day.
It's an ensemble cast and they work together pretty well to show the distrust and maneuvering in the days following Stalin's stroke and death.
The film opens with the Radio Moscow producer in a panic because Stalin requested a recording of that evening's concert, only they hadn't recorded it. So he ran out into the auditorium and commanded the audience and orchestra to stay and perform the whole thing again - bringing in some people from the street to fill empty seats so the acoustics matched the earlier broadcast.
But it turns out the pianist is a dissident and she slips a note in with the record. Upon reading it, Stalin keels over and hits the floor. The next day the housekeeper discovers him still breathing but in a pool of his own urine, and calls Beria (the head of the NKVD). He realizes that Stalin won't last long, and runs around opening the safe, pulling out contingency plans of who must be arrested and shot.
The film is both equal parts black humor and sincerely disturbing, like when Beria has to tell Stalin's daughter Svetlana that he can't release her love Aleksei like she asked, because he was dead (shot on Beria's orders).