How many of the events in The Death of Stalin are based on historical fact?

Death of Stalin is a brilliantly dark comedy but as you state in the question there are some historical inaccuracies.

Apart from Zhukov's inflated rank, the main one is that Beria is shown in the film as at the height of his powers to aid in his portrayal as a menacing villain. In reality, Stalin was in the process of marginalising him, probably with a view to his eventual scapegoating and execution. This was a well-worn pattern that Stalin has followed with former heads of the security services.

The death of Beria at the end of the film is heavily dramatised but broadly accurate. In real life he got a more formal trial than in the film, alongside his subordinates and allies who were co-defendants. His execution was by firing squad rather than a muddled shooting as in the film.

Beyond these inaccuracies most of the events actually happened, including the following:

• The arrest of top doctors following the fabricated 'Doctor's plot'.
• The death of the Soviet hockey team in a plane crash and Vasily's attempts to conceal this.
• Svetlana's defection to the West (albeit later than indicated in the film, in Delhi rather than Vienna and not prompted by Khruschev).
• The perception of Beria as a threat by the Central Committee and consequently their decision to unite and execute him.
• Polina Molotov's arrest and eventual release by Beria.
• Stalin's elaborate state funeral.