Ah, don't you just love a good piece of cake? Breaking Stalin's Nose literally refers to the moment in the book that sets off a chain of events that ends up making Sasha start to call into question the system he has so far blindly accepted. Simple, right?
This kid has quite the imagination, and he really lets it run wild. Unfortunately, a bit too wild, since in his marching around with the Pioneers banner, it "shoots out of [his] hands and its pointy metal tip knocks Stalin's plaster nose clean off his face" (15.11).
The title (along with this central scene) also hints at how Stalin is, ultimately, not all-powerful. It's a facade (although a very strong one) that can be chipped away at. In breaking Stalin's nose, Sasha demonstrates this, although it's accidental.
The eponymous Nose is also an allusion to the Nikolai Gogol short story "The Nose" that Sasha overhears Luzhko (the substitute Russian lit teacher) telling his class. Both Sasha and the main character in "The Nose" experience a disembodied nose running around dressed up in fancy attire. Luzhko's analysis of this story also has important thematic implications for Breaking Stalin's Nose, since he claims it's all about what happens when you allow others to do your thinking for you (if you haven't checked out the character section on Luzhko, go ahead and take a peek now).