When asked about chess books, the school librarian mentions to Beth that they may have a biography of Jose Capablanca. Jose Raul Capablanca y Graupera was a Cuban chess player and world champion from 1921 to 1927.
At 39:03 Beth picks up an issue of Chess Review from Oct 1963 featuring the character Benny Watts on the cover. In real life, the cover of that issue featured Bobby Fischer.
At 24:47, Beth picks up a Sep 1963 issue of Chess Review. Chess Review was published Jan 1933 until Oct 1969. The actual cover of that issue showed the winners of the Piatigorsky Cup, Paul Keres and Tigran Petrosian. The article "USSR Chess Championship" by Vassily N. Panov actually appeared in the Feb 1963 issue. The ad for "Pawn Power in Chess" by Hans Kmoch did in fact appear in the Sep 1968 issue (and many others). The "World of Chess Page" and the "Tournament Calendar" are also real. Chess Review cost 60 cents in 1963.
Alma Wheatley gives Beth a note authorizing the clerk to sell cigarettes to Beth. While needing a note is not unheard of in some communities, it was the norm through the 1970's decade to sell cigarettes to even small children, no questions asked. At this time there were even cigarette vending machines so anyone could buy a pack of cigarettes unsupervised.
The department store where Beth and Alma go shopping for clothes is Ben Snyder Department Store. Founded in 1913, the Lexington KY location on E. Main St operated from 1935-1980, although the building next to it at that time would have been the Ben Ali Theater, not the Lexington Bank and Trust as shown.