Other mistake: Merlin says, "Man will fly someday". For a few frames after he says this, his thumb on his pipe is painted blue, then returns to its normal color. This causes a blinking effect.
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.
Suggested correction: Notice the dialogue just before Merlin turns himself and Arthur/Wart into fishes: Arthur: You mean you can turn yourself into a fish? Merlin: After all, I happen to be a wizard. If Merlin has the magical powers to turn himself into a fish, perhaps a by-product of his magic is that his glasses are magic, so he retains his glasses when he undergoes the transformation into a fish, even if his glasses fall off, they magically return to him, and his glasses magically reappear when he turns back into a human.
What's more likely - the director intended Merlin's lore to include magically retaining his glasses, or the team of animators made a couple continuity errors?
Character mistake: Archimedes says he told Arthur not to pull the sword out of the stone. He didn't, he pointed it out in the churchyard to him instead.
Suggested correction: Archimedes was trying to be helpful when he pointed out the sword so Merlin could take it to the tournament. But after it became a big issue with the rays from heaven and the legend, Archimedes thought he might get in trouble so tried to act innocent by fibbing. It was deliberate and in character, not a character mistake.