this is a know bug and has been covered in many threads here.
If you remove all day events (such as birthdays) it fixes the problem - but you already worked it out yourself.
Some users had to remove 1st April 2013 Easter Monday whole day event.
work around is to change the birthday from all day event to a shorter period of time on that day.
I have a 1 week old iPad and have the same problem. Went to Apple store. The Genius behind the bar told me to update to iOS 6.0.2. Tried that - no update available. Why are some people on this thread asking Apple to please fix it?
This is a £120B cash company charging a lot of money for a product that doesn't work.