While Billie Jean King was having an intimate relationship with Marilyn Barnett during the "Battle of the Sexes", Barnett was not a hairdresser King met by chance. Barnett was King's secretary.
In scene with cheerleaders, Bobby's T-shirt says "CHAUVENIST." The correct spelling is "chauvinist."
The movie starts with Billie Jean King winning the US Open in 1972. She then breaks from the US Lawn Tennis Association along with the rest of The Original Nine. Then the Original Nine get Philip Morris' sponsorship for a women's tournament, the Virginia Slims Tour. In fact, King and The Original Nine broke away in 1970 and Philip Morris sponsored the Virginia Slims Tournament that same year.
While Bobby Riggs is watching television in the Rolls-Royce, he passes channels showing The Mary Tyler Moore Show (1970) and Kojak (1973). Both shows were on CBS but on different days, and neither was in syndication in 1973.
When Billie Jean takes her temperature, she's using old fashioned glass mercury rectal thermometer. Oral thermometers had long glass bulbs, rectal thermometers were short.
When Billie Jean is lying in bed, talking about how she couldn't afford a tennis dress as a kid, she's wearing glasses, but close-ups reveal contact lenses in her eyes.
The images on the monitors in the TV production truck just before and during the final match are simulated. Images shown on professional broadcast monitors of that era either had rounded corners with no gray areas around image or rectangular corners surrounded by gray areas, but never rounded corners surrounded by gray.
Near the end of the match with Billie Jean, Bobby misses a shot from Billie Jean with a racket in one hand and a tennis ball in the other.
When Marilyn leaves the hair salon for Houston, she's shown foiling a client's hair. Foiling was not patented until 1977, so it should have been a frosting cap.
A flyover shot of the Astrodome set in 1973 shows the cylindrical exterior pedestrian ramps which were not built until 1989.
Recreated TV coverage of Bobby Riggs's big matches use the Arial typeface, a knockoff of Helvetica (and similar typefaces) introduced in the 1990s.
In two Los Angeles scenes in a glass elevator, a logo for consulting company KPMG is visible on a building in the background, in the center of the frame. KPMG was created in 1987, when KMG merged with Peat Marwick. The building, now called KPMG Tower, was constructed in 1983.
The scenes in the Bonaventure (including its elevator) take place in1973, but the hotel began construction in 1974 and opened in 1976.