I've heard that historians complaints around the film were that the film doesn't so much take dramitc license to make events seem more dramatic/ridiculous but that the film actually presents an almost toned down version of real events.
I'm not sure which historians you are referring to.
However, take the Death of Stalin with several very heavy pinches of salt.
Let's take one example:
The film's main opening sequence - about the last-minute rushed recording of Mozart's Piano Concerto No.23, featuring Maria Yudina, comes from her associate Dimitri Shostakovich's memoirs -of which the supposed authorship has even been put in question by one of Shostakovich's own children.
Now, even without that source, there are elements of truth to the tale - Yudina was a pianist in the Soviet Union. She has a recording of Mozart's Piano Concerto No 23 attributed to her. Stalin was a known lover of classical music and operas. And as Stalin biographer Stephen Kotkin notes, Stalin was known to spare musicians from the great purges, as he enjoyed their creative outputs.
So, at best, the scenes which tie the opening gambit together could have happened. But even in Shostakovich's supposed memoirs, that incident was some years earlier, well before Stalin's death.
However, I detail this incident, because it shows the style and creative license enjoyed by the Death of Stalin's makers - mixing fact with possible fiction, merging events together, shortening events on the timeline, and, capturing as it does so well, the spirit of the age.
But - and I hate to disappoint - if we were to talk about what the film gets wrong, this would be the longest post in Reddit history.
The film's broad strokes are correct:
Stalin dies in a somewhat drawn-out fashion (taking several days to die, unlike the day or so seen in the film) at the age of 74, in 1953.
The politburo dither, and debate what to do next.
Molotov's wife, Polina, is released from prison.
Khrushchev muscles into power, outwitting his rivals like Malenkov.
Khrushchev has Beria arrested by Zhukov, and then executed, making Beria the last major politician in the USSR to be purged in such a manner.
But the devil, as always, is in the details.
And sadly, we don't have as many primary sources to go on Stalin's death as we'd like. The first-hand witnesses to Stalin's last hours are top Soviet officials, including Malenkov, Molotov, Beria, and Khrushchev and others you see in the film, household staff, Stalin's children Vasily and Svetlana, and the doctors. (It goes without saying that no, the household staff were not massacred outside Stalin's dacha right afterwards).
Perhaps one of the best sources about Stalin's final hours are Khrushchev's own memoirs, which thankfully, have been translated into English. However, Khrushchev's memoirs, as you'd expect, paint Khrushchev in a flattering light and Stalin and Beria in a very negative light.
Here's an extract from Khrushchev's memoirs, the first paragraph or two you may recognise from the film:
"One afternoon Stalin regained consciousness. (I don’t remember exactly which day after his illness began that this happened.) It was evident from the expression on his face, but he still couldn’t speak."
"He raised his left hand and began pointing either at the ceiling or at the wall. His lips seemed to form something like a smile. Then he began shaking our hands. I gave him my hand, and he shook mine with his left hand; his right arm was not functioning. He was trying to convey his feelings by shaking hands. Then I said: “Do you know what he’s pointing at? At that picture.” There was a reproduction of a painting by some artist hanging on the wall. It had been clipped out of the magazine Ogonyok. It showed a young girl feeding a lamb from a bottle. “We’re feeding Comrade Stalin with a spoon, and apparently he’s trying to show us by pointing at the picture and smiling, he’s trying to say: ‘Look, I’m in the same position as that lamb.’”
"As soon as Stalin collapsed, Beria began openly showing his anger and hostility toward him. He cursed him and made fun of him. It was simply impossible to listen to! It’s also interesting that the moment Stalin regained consciousness and it seemed that he might recover, Beria threw himself on his knees beside him, grabbed his hand, and began to kiss it. When Stalin lost consciousness again and closed his eyes, Beria got back up on his feet and spat on the floor. That was the true Beria! He was perfidious even in his attitude toward Stalin, a man he supposedly worshiped and glorified."
Much like how former Wehrmacht generals would go to great lengths after the war to demonise the now-dead Hitler and Goering, instead of themselves, Khrushchev directs almost all his ire towards Beria and Stalin - not towards his still-living former comrades. Beria, in contrast, left no surviving account of his own actions at the time, given that he was dead before 1953 was out.
However, Beria's son, Sergo Beria, in his own recollection of his father, recounts that Beria, in the days after Stalin was ill but before his death, said: "If he (Stalin) had held out a year longer, no member of the Politburo would have survived." And about the crowds attending Stalin's funeral: "He's dead, so what!"
A more intriguing aspect of Stalin's death the film didn't cover was speculation that Stalin was poisoned, possibly by Beria - which would go some length to explain Stalin's unusual last days.
Yet poisoning Stalin would have been no cakewalk.
Khrushchev wrote that in Stalin's last years, the dictator's extreme paranoia had set in. This meant that at the frequent banquets Stalin would hold, he'd ask each Politburo member in attendance to try each dish, and would then "watch and wait" - with the exception of Beria, who was exempt from tasting duties because he had his own meals cooked and served separately at these dinners.
The pen is trickier than the sword
Finally, why are sources on Stalin's last hours so hard to come by? The the chagrin of historians, memoir-writing in the Soviet Union was very difficult. With the party keen to carefully nurture the narrative, censorship was strict, particularly around contentious topics.
Consider the challenges of an veteran Bolshevik writing about what they truly felt:
If you spoke very highly of someone in Stalin's time, there was a likelihood Stalin had had them purged, making them a persona non grata.
If you spoke highly of Stalin in Khrushchev's time, it would appear that you were glorifying the man Khrushchev denounced.
Speak highly of Khrushchev in Brezhnev's time, it would appear that you were glorifying the man Brezhnev overthrew, etc.
(No old Bolsheviks would outlive the Soviet Union and thus the censor, although Stalin's trusty Lazar Kaganovich, seen in the film, almost did - dying about five months before the dissolution of the Soviet Union.)
Further reading:
For us English language-only readers, an accessible source is Simon Sebag Montefiore's gripping retelling of Stalin's death in his book The Court of the Red Tsar. Montefiore quotes sources that were tracked down after the collapse of the Soviet Union and were thus free to speak.