In this book, the most important instance in which Winston Smith records the date comes in the first chapter. This is the point at which Winston begins his diary. When Winston begins the diary, he writes the date -- April 4, 1984.
This is important because of what we are told next -- Winston does not even know for sure what year it is. This is one of the first indications we get about how thoroughly the Party has taken over the society. The Party has kept people in such ignorance that they do not even know what year it is.
When you add this to the slogans and to the names of the ministries and the machine gun nests on the street and other things like that, you can see that the Party has truly taken control of the society and that they have been twisting the truth and keeping the people ignorant.