When the King stops to thank Jack his cigarette is in his right hand. When shown next from a different angle, the cigarette is in his left hand so he can shake with his right.
Princess Margaret is given her "two bennies" in a Pink Gin shown as a garishly opaque drink in a cocktail glass. A Pink Gin consists of a slug of gin with just a dash of Angostura bitters giving it the slightest blush of pink and is totally transparent.
When Elizabeth leaves all the army personnel salute, even though most are not wearing hats. In that case, even for the Monarch, you come to attention, you don't salute. "A salute may not be given unless a soldier is wearing his regimental headdress, for example a Beret, Caubeen, Tam o' Shanter, Glengarry, field service cap or peaked cap."
A corporal would never be an air gunner in the RAF even though at one stage Jack says that he's had his stripes taken off him. Even if he had been a sergeant, the lowest aircrew rank, Jack would not have had the remnants of the upper stripe like portrayed.
Some of the American flags in the crowd are 50 star flags and not 48 star as it would have been in 1945.
While eating breakfast with Jack and her family, Princess Elizabeth is shown holding the fork in her right hand. This is factually inaccurate and would in any event be unacceptable for the royal family at the time.
The bus ticket machine used only came in in the early 1960s. In 1945, tickets were clipped manually.
Royal footmen didn't wear the gold and scarlet state coats during the war. On VE Day they would still have been wearing the blue battledress-type uniforms.
The two main characters are wearing dresses that are from the 1950s, typified by the long, full skirts. These dresses are not just out of period, but they would have been illegal to wear during the wartime due to fabric restrictions, which the royal family were careful to follow, as examples to the nation. Princess Elizabeth's shoes are also not appropriate as leather footwear was not available in colours - again, because of wartime restrictions.
When the Princess and Jack arrive at the air field, we see them driving through a very run down clearly abandoned site, there is paint flaking from buildings and greenery growing from guttering and roadways, suggesting they haven't been used for a long time. While you might expect the site to look 'war torn', you wouldn't expect it to look, disused as it would now.
In 1945 champagne would more likely have been drunk from champagne saucers not flutes. Although we do see Champagne Saucers forming the cascade which Margaret knocks over.
Princess Elizabeth & Jack walk east from London' s West End to the East End across Hammersmith Bridge, which is well to the west of London.
The King tells Elizabeth "This never happened" and "You were at the Ritz all night" when hundreds of people saw her identify herself and Margaret at the Chelsea Barracks. In real life, princesses Elizabeth and Margaret did go out of the palace into the crowds in front of Buckingham Palace that evening and they walked the streets for hours taking part in the celebrations, but they were never recognized. Elizabeth was in her Royal Army uniform and Margaret was only age 14. Elizabeth was a truck driver and mechanic in the Army who actually worked on engines. When they went out that night they were in a party of 16 including several military officers. Elizabeth said later she was terrified of being recognized but they never were and spent hours on the streets. They went out at 10:00 pm and returned to Buckingham Palace at 1:00 am as planned without any incident.
When 'Lizzy' finds a seat on the bus, she has to ask 'Jack' to move his kit bag from the seat. However when he chases after her he leaves it on the bus. No mention is made by him about losing his kit bag when he arrives for parade.