Specifically, his portrayal of the Bolsheviks in Parallel Lives (a joint biography of Hitler and Stalin) seems to show them as largely inept at most areas of government.
They surrendered significant territories to the Germans. They sabotaged the Tsar's unpopular war, but failed to safeguard Russian national territories in the peace negotiations. When the time came to administer the army, the Communists had so little trust in the military leadership that they created a hated commissar system of dual authority.
Their economic policy vacillated between a command economy and free market, causing widespread disruption. Later, Stalin treated the peasantry as a distrusted enemy class. Their industrial output was also prone to number inflation and false reporting, given the pressure to meet set quotas.
Politically, their emphasis on presenting a united parliamentary front to the public (after hashing out their differences behind closed doors) may have led to the later hyper-orthodox atmosphere of fear and intolerance of dissent. This alienated and undermined the intellectual classes, including scientists and technical experts necessary for advancing society.
This was the general gist that I got from Bullock's biography. I think it's been about a quarter of a century since it was published, and on reddit I see posts that portray the Soviet Union as a less menacing society where communism had some strengths as well as weaknesses. Which viewpoint was closer to the facts? If I go with Bullock, it's as though communism was an opportunistic power grab that did nothing positive for the Russians and satellite peoples.
It has been a while since I read Parallel Lives and I'm more familiar with the sections on Stalin's rise to power. I don't recall any great factual errors in Bullock's depiction of the Soviet system. So for example the Bolshevik's definately accepted a harsh deal from the Germans in order to get peace. I think it is still fairly well accepted still that the campaigns against factionalism under Lenin were an important contributor to later issues/impact on inner party debates, the purges etc.
Probably more so what has changed in Soviet historiography would be how we understand the Soviet leadership's thinking/motives. Bullock's depiction of Stalin tends to underplay the ideological aspects, which was common at the time - Stalin was often seen as a master manipulator and opportunist rather than a a dedicated Communist. Stephen Kotkin suggests that one of the great revelations from the opening of the archives has been that Soviet leaders spoke in private much the same way as they spoke in public. So rather than discovering a bunch of cynical people grabbing for power, it seems we found a group of true believers whose policy was motivated by ideology rather than gain. So Bullock's depiction of Stalin amassing power and ruling for his own benefit (or out of some kind of psychopathic behaviour) isn't really in line with current interpretations, which would tend to situation Stalin as acquiring power in order to lead the party along what he saw as the correct/necessary path.
Bullock probably also overplays the role of Stalin, portraying him as being in control of everything effectively. This is perhaps natural though given this was a biographic work, rather than a political or social history. Later portrayals tend to emphasise different power dynamics in the Soviet leadership, with Stalin's grip/methods of management changing over time. So for example Stalin's means of controlling the party-state in the 1930s was pretty different to how it was done post-WWII. These alternate views in turn given more agency to other people/groups in the leadership, as well as regional bosses. J. Arch Getty and Carl Linden being more 'radical' interpretations of those power relations (though Linden was more focused on the Khrushchev era).
Off the top of my head Bullock's interpretation of Lenin's 'testament' is probably out of date. Again this isn't so much that new evidence has been discovered, so much as the interpretation has changed. So for example the document now seen more in terms of personal disputes and Stalin's involvement in the Georgian Affair. Previously it was treated more as Lenin somehow seeing the light and warning the party of Stalin's 'true nature'. I suppose this also follows a bit of a re-interpretation of Lenin, and focusing on his own ruthless activities instead of being seen as somehow betrayed by others (i.e. Stalin's behaviour towards 'factions' really wouldn't have been a huge surprise to Lenin).
For further reading on Stalin there is Robert Service's biography, though this was fairly middle ground and won't go into the changing historiography explicitly. Simon Sebag Montefiore's Stalin biography dips a little bit more into the people around Stalin and is quite accessible, but to me it didn't go far enough into the subject and perhaps lacks a bit of rigour.
Kotkin recently released the first volume of his Stalin biography, however I haven't had a chance to read that yet. You might consider reading Kotkin's "Magnetic Mountain" or Sheila Fitzpatrick's "Everyday Stalinism" - both move away from biography into more social histories. In a sense you'll also get a more rounded view of the Soviet Union by seeing it from a different perspective, rather than always from the view of the 'top'. Kotkin in particular wrote a lot on the historiography of the era in "Magnetic Mountain", so if you wanted a better feel for how interpretations have changed over time that might be the best choice.