2012-142 is valid. 2012-012 is valid. 2012-12 is not. For nth day specify exactly three digits. No confusion with months.

To be precise, 2012-12 is valid and refers to a month. There is indeed no ambiguity.

So how would I refer to the 12:th day of the year?

2012-012. Duh.

I don't see the need for a placeholder for the n-thousandth day of the year. Unless we want to accomodate something like 2011-0367 also equating to 2012-0002?