The woods that Sir Gawain goes through are clearly modern plantations of Sitka spruce (a tree that did not reach Britain until the 19th century), all planted at equal distances apart and all grown to the same size; they look nothing like the old-growth deciduous forests that would have been in medieval Britain.
Sir Gawain passes a gibbet cage, a metal cage used for exposing the body of a condemned criminal, swinging in the wind. However, metal cages of this kind were not used until the 17th century at the earliest, long after the setting of "The Green Knight."
The film is set in medieval Britain, but the spelling used throughout the Green Knight's letter is written in US English. Not only that, but the characters talk about doing things "on Christmas" which is used only in America, English speakers referring to "at Christmas", or "on Christmas day". Whilst it's true to say that the modern English idiom is no more correct for the period, it's peculiar that the director should go to the trouble of using European actors and settings and then be so careless about inserting Americanisms.
The story of Gawain and the Green Knight is set well before the Norman Conquest of 1066AD, however Gawain has breakfast at the mansion in front of windows bearing perfectly rectangular, flat panes of glass. Float glass was only first invented by Henry Bessemer in 1848.
The story of Gawain and the Green Knight is set well before the Norman Conquest of 1066AD, however Gawain has breakfast under a fan vaulted ceiling at the mansion where he stays before going to the Green Chapel. The first fan vaulted ceiling was designed by Thomas Cantebugge for the cloisters at Gloucester Cathedral, built between 1351 and 1377.