When Abbie breaks the Piper's flute in half you can tell that it (the prop) isn't made of actual bone, as bone usually doesn't break with such a clean cut. A break like that is more likely to create long jagged edges.
In the woods, Abbie draws her Glock, there is the sound of a cocking hammer. Glocks do not have hammers.
At the riverside café, the Battleship USS North Carolina can be seen behind Abby Mills. This ship is found at the show's filming location of Wilmington NC, not Sleepy Hollow NY.
The curse is described as "every generation", but when Abbie looks up the abductions on the computer, the dates are far more closely spaced. 1909, 1911, 1913, 1914.