The hill you die on
The hill you die on in relation to films are the small faux pax in films that take you out of the movie completely. Such as the typeface used for a newspaper headline that you know did not exist in the period that the film is set, in this case the 19th century. Other examples include seeing a Picasso painting go down on the Titanic when you know it still exists in a museum, or electronic funds in a heist move transferring via a slowly incrementing bar on a screen, and glasses having plain glass rather than curved lenses in them.
The phrase is a variation of "Is this the hill you want to die on?" which has been used in the military when discussing holding a position at all costs. In this case, the answer is assumed to be "no".