The first scene of "Finding Neverland", is set in 1903, the opening night of James Barrie's play "Little Mary". The vehicle in which Mr & Mrs Snow arrive is a Rolls-Royce model 40/50 HP, also known as a "Silver Ghost". This is an anachronism. The Rolls-Royce company was formed in 1904, with production of the 40/50 HP started in 1907. Moreover, the car has a "Flying Lady" mascot on the radiator which was not designed by Charles Sykes until 1911. The specific car is identifiable from its registration number - BM 8794. It is chassis number 1979, which was delivered new on 10th May 1912. The car used to drive to the summer cottage is a Mitchell Tourer, made in Racine Wisconsin, USA. Although the Mitchell-Lewis Motor Company was founded in 1903, the model in the film appears to be about 1911, judging by the shape and style of the lettering on the radiator. It's certainly no earlier than 1910.
When J.M. Barrie is explaining the concept of the play to Frohman, there is a car approaching them from behind as they walk down the street. The position of the car changes dramatically between shots, though the continuity of the conversation is unchanged.
When the actors are doing the Peter Pan play in the Davies house, just before the wall comes up revealing Neverland, the actor playing Peter's hair is messy, but when she enters Neverland, her hair is neat and tidy.
There was much literary license taken regarding J.M. Barrie and his relationships with key characters. He and his wife didn't divorce until several years after the film's time period. Also, Sylvia's husband didn't die several years after the film; Sylvia didn't until 1910, six years after the Peter Pan premiere. Barrie knew the boys for several years before their apparent first meeting.