When Donna tells the guys that the turkeys have arrived, she points off to her right. In the next shot, the turkeys are to her left.
When the president is explaining what Shibboleth is, he quotes the King James Bible, which varies significantly from the Catholic Bible. Having grown up Catholic, Bartlet would not have studied the King James Bible.
When Charlie leaves the Oval Office after Bartlet gifts him the knife, the sound of the door clicking shut is heard even though Charlie leaves it ajar.
Toby places Jamestown in the 16th century, when in fact it was founded in the 17th (1607).
CJ seems to have no knowledge of the tradition of the president pardoning the Thanksgiving turkey, supposedly because she was sick last Thanksgiving. The pardoning of the turkey has gone on for years before this current administration, and it's not logical that CJ would not be familiar with the tradition.