Continuity mistake: When Merlin is thrown in to the armor under the water as a fish, his glasses are thrown off and they land on the nose of the armor. The next time they show him, the glasses are down beside him. And still again, when Merlin is changed back into a human, he has the armor on his head and when he pulls it off, his glasses are on underneath the armor.
Continuity mistake: Arthur jumps over an enclosed fence to get to the Sword in the Stone. After he gets the sword, he runs out of an opening in the fence that wasn't there when he entered the area.
Continuity mistake: When Kay tells his father that he is now "Sir Kay" at the banquet celebrations in the castle, there is an eaten chicken and bones in front of him on the table that disappear in the very next shot.