Hehe. I wish I knew more.
Charlie: Gibson wasn't known for keeping organized serial numbers. It's a mess today, with about 8 different serial numbers floating around. Even though yours comes up "No Entries" for the production date. It does fall in line with serials from 1966. It's highly probably that it was made in '66. But like I mentioned, take some pix - front of headstock including the Gibson logo, back of headstock with serial, if you are adventurous, remove the pups and look for any writing in the pup cavities. There should be something there. Less likely to find any info in the back control cavity, but you can poke around in there too.
Re: Dots on fretboard. Its possible the neck was replaced at some point. When did you buy this LP?
With I could be of more help. Good luck!
Dave