In The Old Grey Hare, the future is depicted as an inevitable extension of current rivalries, projected into the then-distant year 2000. Following an existential breakdown by Elmer Fudd, a celestial voice transports him through the decades to a world where he and Bugs Bunny are elderly, wrinkled, and physically frail, yet still locked in their perpetual cycle of hunter and prey. The setting is less a reimagined society and more a comedic backdrop where the laws of cartoon physics have aged alongside the characters, featuring a world where the "year 2000" is defined by the endurance of 1940s pop-culture grudges.

The societal and technological dynamics of this future Earth are framed through the lens of mid-century satire. The film suggests a world that has moved past traditional television into more sensory-focused media and where personal weaponry has evolved from shotguns to "Buck Rogers" style ray guns. This future appears to be an alternate timeline where the aging process is slowed or the characters possess a form of hyper-longevity, as they remain active (albeit with lumbago and canes) nearly 60 years after their prime. Earth itself remains recognizable as a wooded, natural landscape, implying that despite technological leaps, the fundamental environment and basic human (or rabbit) impulses remain unchanged.

Specific predictions in the film include "Smellevision," a gag predicting the replacement of television with olfactory-based broadcasting; while smell-based cinema (such as Smell-O-Vision) was trialed in the 1960s, it never achieved the predicted ubiquity. The film also features a "Lightning Quick Rabbit Killer" ray gun, a precursor to modern directed-energy weapon concepts. Additionally, a futuristic newspaper headline jokes that "Bing Crosby’s Horse Hasn't Come In Yet," accurately predicting the long-term cultural footprint of 20th-century celebrities, even if the specific equine investments did not literally span six decades.