It's of no importance, but I think the broadcast date must have been either January 1 or January 8, 1967. Those were both Sundays, and everybody on the show is wishing everybody else a happy new year--even in the ads. (And it had to be some date after the October 1966 opening of The Apple Tree and before the March, 1967 release of Hurry Sundown.) All the "happy new years" seem to make January 1 more likely--unless the "football game next week" that Allen Ludden refers to near the end was Super Bowl One, which was played on January 15, 1967.
As I said, it's of no importance, but I always enjoy trying to figure out the dates of undated clips from their internal evidence.