I was around and fairly aware in 1963 and think most people didn't start worrying about Vietnam till about a year later. But I may not remember correctly. I do think there are some anachronisms in the show. Most of the writers are too young to remember (or know) the exact chronology of things. They may only be a few months off but if you lived through it, that's important to you. (Eg I think they have someone going to a Dylan concert and everyone knowing who Dylan was in 1962, whereas he was not very well known outside of Greenwich Village until The Freewheelin' came out in May 0f '63. Didn't his first record sell only 5,000 copies?)