Near the end of the film, when Helen is wearing the red dress, Charlie comes home drunk and puts the chain on the door. The chain is a lot longer than a normal door chain, at least 12 inches. When Helen comes home later and tries to get in, the chain is now much shorter. It's now the length of a normal door chain.
When Helen is hospitalized for the second time (about 1.5 hours into the movie) an oxygen tent is rolled into her room but when Charlie goes into her room the tent is nowhere to be seen.
At the beginning of the film Van Johnson arrives at a train station carrying a suitcase. He hails a cab. Shortly thereafter he exits the same cab sans suitcase. It is not seen again.
When Charlie sits down at the park on his first visit there with Helen, a balloon seller who was not there previously appears behind them.
When Helen tells Charlie that they should go home to the USA, in one shot Charlie is facing her and grabs her upper arms, and in the next he is no longer holding her arms and is off to her right.
In the title screen at the beginning of the the movie it says "COPYRIGHT MCMXLIV IN U.S.A.", which in roman numbers is 1944, but the film was released in 1954, in roman numbers would be MCMLIV.
The flashback originates from a newspaper headline reading "U.S. TROOPS IN PARIS," over a photo of American soldiers marching through the Arc de Triomphe. The newspaper headline and photograph date from the liberation of Paris in August 1944. This 1944 photo then transforms into the beginning of the flashback, which is set not in 1944 but on V-E Day (May 8, 1945).
Charlie and Helen are waiting to see the lights of Paris turn on when the large crowd starts singing a song in unison. There is a close-up of an older, grieving woman crossing herself by the War Memorial while a soldier and a younger woman behind her are singing along with the crowd, but their lips are not moving correctly with the lyrics.
At 00:38:00 when Helen swings the baby in the air and says "No guts, eh?" her lips aren't moving.