Darth Vader vs. Gandalf - S1-E2
Continuity mistake: After Gandalf turns himself into the image of Anakin, he uses a Force push against Vader. In the first shot, his arm is fully extended with hand open out. But it then cuts to a different angle and instantly his hand is half closed and arm already bent to come back. (00:06:25)
Darth Vader vs. Gandalf - S1-E2
Continuity mistake: As Gandalf and the Hobbit, who I assume is supposed to be Frodo, are first seen walking up a hill, Frodo is lagging behind some. It cuts to a reverse angle and suddenly Frodo is right up behind Gandalf. (00:04:10)
Darth Vader vs. Gandalf - S1-E2
Factual error: When Gandalf is first shown, it says that Lord of the Rings is the third bestselling novel of all time. At the time of filming (and still in 2013) The Lord of the Rings was the second bestselling novel of all time. (00:01:40)