When Alex wakes up and watches one of Morgana demons climbs out of the ground from his window, his alarm clock reads 1:00. After Merlin defeats it in his bedroom after it tries to kill Alex, his clock still reads 1:00 even so a few minutes should have passed. In addition, when his clock reads 1:02, early daylight can be seen lighting up his house, even so it should be at least four hours before dawn begins to break.
Throughout the movie they are counting down to an upcoming solar eclipse. Yet the Moon each night gets more and more full with it being completely full the night before the eclipse. A solar eclipse can only happen on a new Moon approximately two weeks away from a full moon.
Merlin's Led Zeppelin shirt continuously changes between gray and black between shots at different points of the movie. Edit: This is an intentional choice as it goes from dark gray to light gray depending on Merlin's age; when he looks younger (while being older) the shirt is darker because it has faded as the shirt is old. When Merlin looks older (while actually being younger) the shirt is bright gray because it's newer and hasn't faded with time. This is because Merlin ages in reverse and the clothing represents that visually. It is not a continuity error.
When Alex is fighting Lance in the lake, he falls into the water and completely submerges. Immediately after Lance walks away, Alex takes his King Arthur book out of the back pack he is wearing and it is completely dry, despite the backpack being an ordinary school bag and not waterproof. When Alex falls (0:58:02 to 0:58:35) he falls on his stomach and the top of the backpack remains out of the water. Moreover, at 1:01:29, Bedders suddenly exclaims "We're dry!" Presumably, the "magic powers" could keep the book dry if need be.
When the science teacher has his students hold their paper-mache models of the sun and moon to demonstrate a solar eclipse, he said: "...when the two planets align". Any teacher should know that the moon and sun aren't planets.