The NYPD Mounted Unit was never disbanded and has been in operation from approximately 1858 with a formal title since 1871.
The other officers say that Schnauser joined them 10 years earlier. That would be 1952. Yet all the cars, including the car Muldoon is acquainting Schnauser with, are late 1950'sor early 1960's models.
Muldoon tells Schnauser to put the car in neutral, turn the key , and hit the accelerator. He never mentions shifting the transmission into Drive.
Even though the story takes place ten years in the past, everyone looks exactly the same, and everything else, from the cars to the clothes to everything, is the same as the current day. Hilariously, not a single bit of effort was made to make anything appear as it was ten years ago.
The horse riding stable that bought Sally the Horse is supposedly in midtown Manhattan, and near Central Park. However, right outside the door of the place there is a sub-level highway, and there are none of those in Manhattan, let alone near Central Park.
Sally the horse, referred to as "she" is clearly a male.