Ichabod Crane was a bachelor in The Legend of Sleepy Hollow, so he would not have grandchildren of any kind, as Beth claims. But the Crane of this version might not have had quite the same biography as his Washington Irvingian counterpart.
Sleepy Hollow looks nothing like it does in the episode, though large mansions like the one seen in the episode do exist in that part of Westchester County.
After he crashes the Halloween party and sends the guests fleeing in terror, the Headless Horseman is seen galloping away from Crane Manor. Despite this, Scooby and the gang start searching for him inside the manor instead of the outside grounds.
Scooby Dum is described as Scooby Doo's brother and cousin at different points in the story.
When Velma says Shaggy found the most important clue, Shaggy says "yeah" in his normal voice, and then says, "I did?" in another voice.