These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Adaptation Displacement: The movie is much more well-known than the play, even though the opening credits actually state in big letters what it was based on.
Genius Bonus: Many historical events mentioned in the movie are real. The song sung by minstrels before Bunsha interrupts them is an actual old Russian song about the battle of Molodi. The Crimean khan's troops marauding near Moscow is an actual event from that same war (though they mixed up the order in which those events happened). The cruel and unusual execution by barrel of gunpowder also happened, with the exact same phrase uttered by Ivan IV, though the victim was a seditious aristocrat, not an inventor.
Older Than They Think: The Kremlin shown in the film is made of white stone, which is its original look. However, it was rebuilt to its current "red brick" look by Ivan the Terrible's grandfather Ivan III.