We almost had an extra summer month
We already know the daylight savings time makes no sense. And then there's Leap Year, and the fact that all the months are different lengths.
Apparently, calendar wonkiness have been a point of contention for millenia leading up to and long after the Gregorian calendar. Gizmodo covers the history and why's of the calendar. Most recently, a 20th century reform was attempted by one Moses B. Cotsworth, who would have made all the months exactly four weeks long and add a 13th month called "Sol" between June and July. This did not catch on. The full history, here.