In the newsreel scene from 1936 showing the funeral procession of Edward's father the King, the voiceover announcer says that "King George the Third has died and the nation mourns". It should of course have been King George the Fifth.
In "W E." Edward and Wallis are shown riding horses together (Wallis wearing a kind of dressage outfit): Wallis did ride on the U.S. and in China, but there's no evidence that she went riding with Edward in England.
At the start of the film (2'40), Wally Winthrop is shown taking a bath. When she turns on the bath taps (faucets), the plug is clearly hanging down but in the next shot it is plugged in.
When Evgeni leaves to go find Wally, it is nighttime, but when he finds her, there is daylight coming through the windows of her room.