Symbolism, Imagery, Allegory
The dates in the diary entries start out looking completely normal, but when Poprishchin starts to think he is the king of Spain (12.1), they get increasingly strange (or just don't exist). These dates are very important because they are mileposts on Poprishchin's journey into madness. Since Gogol likes to keep us guessing—how crazy is Poprishchin, exactly—until the very end, these mileposts remind us that Poprishchin is gradually losing it.
The confusion of the later dates ("86th of Martober" [13.1] or "January of the same year which came after February" [18.1]) also symbolizes how confusing life was starting to get in Russia, especially if you had a job where you had to measure and keep track of things. Confusing how? Well, first of all, there was the difference between the Russian units of measurement, area, volume and weight and those of continental Europe (yes, you guessed it, the metric system).
And how about this: on top of all that, during Gogol's time, Russia was still following the Julian calendar, which meant it was always about 13 days behind Europe, most of which was on the Gregorian calendar.
So when someone like Poprishchin read about, say, the affairs of Spain in the newspaper, he would have to keep converting between the Gregorian and Julian calendars. Quick: what's Fourth of July in the Julian calendar? It could make anyone go crazy.