Eloise (Sofia Vassilieva) has teeth that are clearly not those of a six year old.
In the scene in which Eloise is playing a piano duet with the Plaza's pianist, it can clearly be seen that they are playing a Young Chang piano. However, the Young Chang piano company was not even founded - in South Korea - until 1956. The odds of the Plaza using a Young Chang at the time this movie is set seem extraordinarily low.
When Eloise is looking in the Window of FAO Swartz you can see a Poster for Aida in the background, a play that did not premiere on Broadway until 2000.
When the police cars arrive at the Plaza there are modern taxi cabs in the back.