After a dance class, Alison asks Molly if Emily would come over for some tea. When Alison taps Molly's shoulder, she uses her left hand. When the view switches to Molly, she's using her right hand.
When Alison taps Molly's shoulder inviting Emily to tea after dance class, Molly puts her glasses on and takes her hands off. When the view switches back to Alison, Molly still has her hands on her glasses.
The scene shows Molly hugging her teacher and her arms are around the teacher's shoulders. When it zooms up however, Molly's arms are around the teacher's waist.
"Senator Claghorn", the character Molly listens to on the radio, didn't make its debut until October 1945, after the war had ended.
Molly's saddle shoes are inaccurate for the time period of 1943. Black and white saddle oxford shoes in this time had coral soles. The shoes that Molly wears in this film have white soles. White soles for saddle oxford shoes were not introduced until the 1970s.
The furniture in the family's living room is not 1940s furniture. It is from the 2000 decade but sort of in an Early American style, what you find in mobile homes. Looks totally out of place for a 1940s movie. Some of the street signs in the movie are modern signs, not from the 1940s.
A film crew member holding a microphone rig can be seen in 43:17 to 43:19, i.e. the scene where Emily is attending classes at Molly's school and is asked by her classmates if she knows then-Princess Elizabeth and the royal family.
When Miss Campbell introduces her fiancé Lieutenant Davies to Molly and her friends, he wears infantry branch insignia on his uniform (crossed rifles lapel insignia and a blue Combat Infantryman's Badge above his breast pocket), but later Molly and her friends tell her mother that Lt Davies is in the Air Force.