I know it's always bothered me that they don't line up anymore, so I was wondering what the Romans thought of it? This is a bit of a strange question, I know.
I've read that this threw the date of the "new year" off, and those who didn't realize/forgot were called "April fools". Is this just an apocryphal explanation of the origins of the day?
The introduction of January and February was attributed to Numa Pompilius - which in practical terms means it was so long ago that nobody really remembers it ever having been any different and not at a time from which there were written records.
Roman writers remark on the fact that these months were obviously added into a 10 month calendar and form different theories on it (e.g. Ovid wants February originally to have been placed before January; makes more sense to have a time of expiation at the end of the old year) but they aren't confused/irritated in any way.