The opening scene is an establishing shot of Broadway, labeled "1955". However, a movie theater marquee can be seen advertising 1948's BF's Daughter and none of the cars is of a more recent model than late '40s.
When on the beach in Coney Island, they show the Cyclone roller coaster and the parachute which would have been there in the 1950s. However, adjacent to the roller coaster is the Astroland Tower which would not have been built until the early 1960s.
On Bettie's trip to NYC we see historically accurate Greyhound buses, most likely the 'Silverside' model built in 1948. The problem is the scene when her bus enters the terminal in New York. The bus is distinctly a General Motors GMC PD 4106 model, which didn't enter service until 1964.
The film depicts Bettie as being OK with the fetish/costume/bondage modeling - and being quite naive as to the erotic uses of such photos. This is exactly opposite from how the real Bettie Page felt about modeling. Her attitude basically was that "God made us nude, so how bad could it be?" but the more extreme fetish posing fostered sexually deviant desires. The numerous fully nude shoots she did for amateur camera clubs bears this out.
When Bettie first meets future husband Billy in the park, she makes the statement that she'd seen Billy play football against Hume-Fogg high school. In reality, she and Billy both attended Hume-Fogg in Nashville, TN.
In one 'bondage shoot' scene, Jared Harris shoots the bound Betty with a Leica camera, lens retracted. Collapsible lenses on Leicas need to be extended to shooting position for proper focusing. Shooting with a lens retracted will result in blurred pictures, and all photographers who shot with Leicas should know that.
In the scene mentioned above (with the improperly used Stereo-Realist), many photographers are seen using simple 1940s-50s box cameras indoors. No large window or strong artificial lighting seen. Yet, the photographers were shown shooting with ease, as if they were shooting outdoors in bright light. In the 1950s, box cameras and the less sensitive films can only be used satisfactorily outdoors in good light.