One small question, when did October 15 become the next day after October 13? A minor typo, there, methinks.
Author's response
Nope, on purpose. The 13th was a Saturday (really, not JKR's silly 'September 1st is always a Monday calendar) A Victorian society like the Wizarding world wouldn't have a Sunday paper, so the first Rita could spread her rumors would be Monday the 15th.