Vintage Cars: 1967 oldsmobile cutlass, oldsmobile cutlass, pilot models

Question
Is it possible that a 1967 Oldsmobile Cutlass that was built in the 3rd week of October, 1966, could have a VIN
that is titled as a 1966

Answer
Of course, ANYTHING is possible.  What we need to consider is what's "probable."  

Manufacturers today introduce new cars when they're ready, and rarely wait for the traditional fall season.  But back in the 60's, they rarely strayed from the norm, which was to roll out all the new models in late September- early October.  To do this, they needed to start producing pilot models (the first few cars made to get the bugs worked out- these cars were rarely sold to the public) sometime in August, with full production underway around Labor Day (again, there were always exceptions).  The '67 Cutlass was pretty much a "carry-over" model from '66, with a few cosmetic changes.  So, I've got to believe that a car built in the 3rd week of October had to be a '67, not a '66.

Now, are you saying you have a car like this- built in late October with a '66 title?  If you do, I see four possible explanations:
1) the factory entered the wrong year on the paperwork, and the dealer didn't catch it (virtually impossible);
2) the state in which it was titled made an error when issuing the title (highly unlikely);
3) the dealer made an error in creating the sales paperwork, one which allowed the year "1966" to appear on the title (not likely, but still possible);
4) the year got switched when doing the paperwork AFTER the car was sold new, between two of the previous owners (the most likely of the four).

It's even possible that something else happened to cause this, but to answer your original question: my personal opinion is that it would have been nearly impossible for a 1966 Olds to have been built in late October of 1966.