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Anachronisms
The end credits credit the "Courtesy of" section for "Street Fighting Man" by The Rolling Stones to ABKCO Music and Records. "Street Fighting Man" was not reissued by ABKCO until 2016.
When Mr. Fox looks out the tree's window and notices the distant Boggis, Bunce and Bean farms for the first time, they are lined up in that order left-to-right on hilltops. But when he later shows a map of the farms to Kiley, the Boggis farm is clearly situated between Bean and Bunce.
Early in the movie, Mr. Fox sits at the breakfast table with a newspaper. In it, he notices a picture of a tree for sale, which has landscape (horizontal) orientation. When he cuts the picture, he does so as if it was a portrait (vertical orientation). In the next scene, he holds the clipping up, and it is in landscape orientation again.
Frank Bean, inside a caravan, on the phone says "They took everything, let me call you back Petey." After a quick burst of anger he exits the caravan, and Petey is sitting right outside fixing a bike, without a phone (not that you'd talk to someone on the phone who is right outside anyway).
On Clive Badger's desk there is a single paper clip near the pen-holder. But in the reverse view on Mr. Fox, the paper clip is missing.
In long-shots, there is a building between the second and third of the four silos on the Bean farm ("E" and "A"). In closer angles, the silos are equally spaced and the building is not readily visible.
At the shooting, Boggis's double-barrel shotgun fires at least five times in quick succession without re-loading.
When Latin names of the animals are displayed in the film they are not written in the correct format. "Latin" names, more correctly termed scientific names, are standardized within the scientific community worldwide and written in a specific format, e.g. Genus species with the genus capitalized, the species written in lowercase, and both written either in italics or simply underlined. The film shows both genus and species capitalized.
The rabid beagle's tag reads Canis familiaris, an obsolete classification. Tame dogs (familiaris) are now considered to be a subspecies of the wolf Canis lupus (which Fox correctly identified on the mountain), rather than their own species. Since news of species revisions travels slowly, it is realistic that not everyone has heard of the change.
After 1h15min, when Mrs. Fox mentions that she is pregnant again, one scene is an CGI picture with little detail.
The end credits credit the "Courtesy of" section for "Street Fighting Man" by The Rolling Stones to ABKCO Music and Records. "Street Fighting Man" was not reissued by ABKCO until 2016.
The film is clearly set in England, according to Mr. Fox's morning paper and other clues. However, the wolf's alpine backdrop more resembles the Canadian Rocky Mountains and Kylie is a North American opossum. There are no opossums or any marsupial relatives native to Europe. On the wackbat trophy's champion list, there is an "M.K. Silvery-Marmoset" which is a creature found only in very limited areas in Brazil.
Rickity's species is a meadow vole (Microtus Pennsylvanicus), which is not native to England, but is instead native only to northern North America.
Ash says he doesn't have a bandit hat but a modified tube sock, but the hat/sock he puts on has a clearly visible heel, identifying it as a crew, rather than a tube, sock.