Perhaps you've heard of the 'y2k bug', where software wasn't ready for dates rolling from 1999 to 2000. Turns out NASA's space shuttle software has a d366 bug every new year's eve:
NASA wants Discovery back from its 12-day mission by New Year's Eve because shuttle computers are not designed to make the change from the 365th day of the old year to the first day of the new year while in flight.
The space agency has figured out a solution for the New Year's Day problem, but managers are reluctant to try it since it has not been thoroughly tested.
I'm surprised NASA's space systems care about calendar years at all. I would have expected them to use some other reference frame, like say seconds since the moon landing.