Well, there's another mistake:
The car is a Fiat 501, predecessor of the 503, which was made between 1919 and 1925. No way that scene could have been shot in 1927. Michael was born ca. 1919, and, as you point out, he's 3 or 4 years old at most in that scene. If Connie was 18 in 1945, she'd have been born in 1927.
Are you sure it's a 501 and not a 503? The cars are almost identical. How can you tell? And why else would the DVD say it was 1927?
According to that car database this is a Fiat 503.
Here are some photos of the Fiat 501 and 503.
Fiat 503:
Fiat 501:
