Nick Arnstein meets Fanny for the second time on the night of her debut with the Follies, which was in 1910. When she walks him to his car, we see that it is a Rolls Royce Silver Ghost with the famous Spirit of Ecstasy on the radiator, a mascot which would not be produced until the following year.
In the famous "tugboat scene", Fannie rides out on a New York Central tugboat painted jade green - a color which wasn't instituted on the boats till the early sixties. To be accurate, the tugboat would have to have been painted red with a black stack and the New York Central logo.
In the movie before Fanny and Nick married in 1919 she had followed him from Baltimore to New York City to head to Europe aboard the R.M.S. Berengaria. Originally that ship was part of the Hamburg-America line and was christened the S.S. Imperator; it was not until late 1920 that she was re-christened R.M.S. Berengaria when she was taken over by Cunard as part of war reparations.
In the sequence where a telegram is brought to the Brice saloon, the camera closes in on two ladies, one of whom says, "That's life for you: somebody's dead." She wears a skirt with gray and white stripes, a cream blouse, and a straw hat with a pink and green ribbon. As the camera follows the Western Union delivery man, the same outfit can be seen on a different bystander.
When Nick and Fannie leave the lobster restaurant in Baltimore, the sun is setting over a large expanse of water, with no land visible, presumably the ocean. A sunset in Baltimore would be over land (west) rather than the ocean (east).
When Fanny runs out to greet the ship she expected to board at the last minute to meet Nick, she's seen at the East River. She boards a tugboat with a clear view of the Manhattan and Williamsburg Bridges in the background. In fact, all steamships then, and cruise liners now, leave from the west side of Manhattan -- from the Hudson River where at the time, there were no bridges to be seen. Now, the only bridge on the Hudson (and not yet built (1933) would have been the George Washington.