I didn't end up finishing the exam, but I wrote very similar things for Russia as you guys! Only got two bodies in, but my points would have been..
1. Stalin having control of the party machine prior to lenins death as general secretary essentially giving him a leg up…what with all the new Bolsheviks that owed their job to him
2. Stalin as well remaining as a grey blur rendering him a blank slate where he can manipulate his political opinions and form alliances to enhance his power. I mentioned Zinoviev and Bukharin, because I could not remember much from his alliance with the right faction
Didn't get to the third point, but I would have mentioned the differing ideologies on economics and interpretations of Marxism. Ie, permanent revolution vs socialism in one country