Certainly in all major societies there is an official keeping track of what date it is, and perhaps they accidentally skipped a date, for example. Are there any recordings of skipping, by accident or purpose?
There have been several methods of keeping time. Two of the most well-known of recent times are the Julian and Gregorian calendars.
The Julian calendar is named after Julius Caesar, who ordered the adoption of a certain calendar system (it had the same months and days but inserted leap years according to a different rule), and so it fell behind after a certain amount of time. The difference was that the Julian calendar was 0.002%. This introduced an error of about 1 day every 128 years. Naturally, over time this became a significant difference.
The Gregorian calendar was a reform that adjusted this to be more accurate. We are currently using the Gregorian calendar today. Now the error is 1 day in 3236 years.
However, countries adopted the Gregorian calendar at different times, resulting in some cases in weeks missing from the year.
France switched in 1582, and skipped 10 days, while Russia switched in 1918 and skipped 13 days ahead. The United States skipped 11 days when they switched in 1752.
http://www.timeanddate.com/calendar/julian-gregorian-switch.html