In the John Wayne movie Rooster Cogburn (1975), there is a dramatic focus fall off at least 10% of the vertical height at both the top and bottom of the lens. Why does this happen?
This is most likely caused by field curvature. Whether it was introduced when the footage was shot or later when the film was digitized or even when converted to the still image above is impossible to say from only looking at the sample image above.
At the time Rooster Cogburn was filmed plenty of lenses did not correct very much for field curvature. This might particularly be the case for lenses selected by a cinematographer for use to film mostly outdoors in daylight the way most westerns were shot.
In the 1970s budget considerations were often tighter for westerns than other types of films. The marquee value of the actors, rather than pure cinemagraphic quality, drove the box office performance of a genre that was fast falling out of favor with the moviegoing public. With the fairly narrow apertures used in daylight shooting conditions the effects of field curvature could be largely ignored. The photo above, however, was likely a single 24x16mm frame from footage shot in a much dimmer environment to simulate an indoor scene and the aperture would have probably been opened up more than would normally have been the case for most of the other scenes in the film.
Although as of late field curvature seems to most photographers to have become an undesired aberration to be avoided at all costs when considering a new lens, there are times when it is a desired quality for getting a shot to look a certain way. For the photographers who are in the know about what such a lens can do for certain types of shots field curvature isn't necessarily a problem at all.
The demise of the attractiveness of lenses with field curvature seems to be the current obsession with how sharply a lens can photograph a flat test chart as seemingly the only criteria upon which to base a judgement of a lens' quality. When the center is in best focus, a lens with field curvature will look softer on the edges. That doesn't mean, however, that the lens is really 'soft' on the edges. It just means that when aiming at a flat test chart with the center of the chart in sharpest focus the focus distance at the edges is somewhere in front of the surface of the chart. With some very high quality lenses that are designed to have field curvature, the edges of a flat test chart can be rendered very sharply by adjusting the focus distance. Of course this makes the center of the flat test chart slightly out of focus and now the center looks a bit soft!
In the case of the example image in the question, the field curvature appears to have an oval, rather than circular shape. This would indicate that the lens used to film the scene and any lenses used to convert the film to a later format were anamorphic lenses.