In the last scene of the third act, when the Headless Horseman picks up a head to complete his disguise as a motorcycle cop, the face is clearly clean shaven in the close-up, but has a short stubble when he puts it on a second later.
Jenny says she was 12 and Abbie was 13 when they first saw Moloch in the forest, however it was previously established that Abbie is 3 years older than Jenny because they said Abbie was 6 and Jenny was 3 when their dad walked out on them.
At approximately 15 minutes, Jake Wells stated that Benjamin Banneker's writings burned in a fire in 1826. According to encyclopedia.com, the fire that destroyed most of Banneker's personal property, including his writings, actually occurred on the day of his funeral and burial, October 11, 1806.
At approximately 32 minutes, Agent Diana Thomas stated that as part of the decoys to protect the president, Air Force One was in the air. At the time, though, the president was in the White House. The president's plane is only called Air Force One when the president is on board, so it wouldn't have been called that.
Alex states that she removed a hair follicle from Ichabod's jacket and sent it for Carbon 14 dating, then proceeds to list a number of results, none of which are determined by a Carbon 14 test.