Beth is sent to Bradley's by Alma with a note to get 3 packs of Chesterfields. The clerk hands her just one pack, which is seen again when she looks at the chess magazine and again when she walks out of Bradley's. Yet when she arrives home, she places 3 packs down on the kitchen counter.
Between two strong chess players, by far the most common result is a draw, however draws are rarely even referred to throughout the series and Beth is never shown drawing a game.
Algebraic chess notation (i.e. a1-h8), which appears frequently throughout the series, was rarely used by English-speaking players in the 1960s, descriptive notation (e.g. P-K4, N-KB3) being the prevalent notation. However, for strong English-speaking players to keep up with developments, familiarity with algebraic notation, the predominant form in European and Soviet chess literature, would have been essential.
Characters throughout the series mistake Beth's age. According to time stamps given throughout the series her age should be 15 at the time of adoption and winning her first and second chess tournaments in 1963. In 1966 she would 18, and by series end 20 years old.
Throughout the series, the age Harmon was first taught chess is sometimes given as eight and sometimes nine.
When Beth returns to her house from various travels, her suitcases seems empty.
Beth is seen dancing to Venus by Shocking Blue in her house. Much later in the episodes she is shown to visit Moscow in 1968. Venus didn't come out till 1969.
Much of the music played on the piano by the stepmother is by French composer Erik Satie. Although Satie had died in the 1920s, his music went into obscurity until it was rediscovered in the mid-1960s. It is highly unlikely that the character would have been able to find his music in a Kentucky music store in the 1950s.