Although both Abbie and Crane discuss Thanksgiving as if it were a common annual occurrence, Thanksgiving in the US was not as regularly celebrated in his time. The first Thanksgiving was in 1621, the second in 1623. During revolutionary times, several Thanksgiving days were declared. George Washington declared the first national Thanksgiving Day (a one-time event) in 1789, followed by Adams and Madison declaring Thanksgiving days during their presidencies. New York was the 1st state to adopt an annual Thanksgiving in 1817. Lincoln declared it a national holiday in 1863.
When Ichabod is telling Abby that the Pilgrims did not eat turkey he says "it would have been a miracle if a half starved Pheasant walked by". Pheasants were not introduced into North America until 1881 however.
When Abby and Crane find the bodyguard's corpse at Fredericks Manor, Abby wants to go outside to radio for backup. When the door slams shut in her face, for a split second you see a crew member outside.
The show is set in New York, yet the scenery is full of Spanish Moss which only grows in the Southeast, such as coastal North Carolina where the show is filmed.