Good question. In the library, intercalary days are just their own month. So it would just be 2015-14-1.

In other words, there's actually a 14 month that either contains 1 or 2 days, both of which have no weekday associated with them?

I don't see how it would make things much easier, especially for timestamps in various date formats and date-input fields.

Why? It's still three numeric digits. If anything, it would be much easier to calculate date validity. In Python:

  acceptable_days = range(1,29)
  if pickedMonth == 14:
     acceptable_days = [1];
     if isLeapYear(year): acceptable_days = [1,2]
     # any future hack will just go here 
  
  if pickedDay not in acceptable_days or pickedMonth > 14: 
     raise InvalidDateException()  

Compare this with anything we use today. Which code is simpler?

2015-00-00 2015-00-01

And making dates 0 indexed will make all the C-weenies happy.

Are you saying you'd put the extra days at the start of the first month of the year? Wouldn't that put you back to where the days are not consistently ordered based off their position in the month?

The extra days don't advance the Sun-Sat cycle no matter where you put them. January 1 is essentially defined as Monday (or whatever).