Dick Yarmy, who plays the Director, is the brother of Don Adams of Get Smart (1965) fame (whose real name is Donald Yarmy).
Throughout the run of the show That Girl did not comment on many of the more serious social situations going on within the United States. During the middle of this episode, however, Ann wears a red shirt with the word "peace" repeated in the middle of the shirt giving a small nod to the Vietnam antiwar movement. Later in this season both Ann and Don wear items of clothing with peace symbols.
The translation of the title of the episode is actually not the title of the series: "that" is not a Spanish word, the other word means "damsel." The correct translation for 'That Girl' into Spanish would be, 'Esa Chica'.
Don and Anne discuss investing in the stock market and returns over ten years. In fact the Dow Jones Industrial Average fell significantly from 1970 to 1980.
Ironically, Alejandro Rey, playing the Mexican actor/activist who objects to the offensive portrayal of a Mexican woman by a non-Mexican actress, was actually Argentinian.