One such example occurs in Harry Potter and the Prisoner of Azkaban when Sybill Trelawney refers to 16 October as Friday, although 16 October 1993 was a Saturday.
This is usually explained as artistic licence on the author's part.
Although the series, according to the timeline derived from the Chamber of Secrets reference, is set in the nineties, the series often seems as though it is set in the late nineties to mid-2000s, roughly concurrent with the publication of the books.
In Harry Potter and the Half-Blood Prince, Cornelius Fudge uses a male pronoun to refer to the "predecessor" of the Prime Minister of the United Kingdom.
Since the celebration was commemorating the five-hundredth anniversary of Nick's death, this seems to say the scene takes place on 31 October, 1992. Rowling confirmed, via her Twitter account that that was the day the Epilogue was set.