When Amy arrives home after school on the day the test reveals her as a witch, she walks through a short gate in front of her porch and slams it closed. In the next shot, you can clearly see the gate behind Amy and it is standing wide open.
Cordelia gets out of the Driver's Ed car and shuts the door. In the next scene, the door is open, and when the truck hits it, it slams the door shut, although the door was, as far as we have seen, already shut.
When Xander and Willow are talking in the hall about his invisibility, the pen Willow toys with changes position back and forth between front and reverse shots.
While Buffy, Willow and Xander are in the lab making the witch revealing potion, Willow pours the finalized mixture into a test tube and fills the tube half way to the top. When Buffy takes the tube, it is barely a 1/4 full.
At home, Buffy helps her mother open a crate. She tears off the cover and leaves it hanging by the side. Next shot, the lid is back on. Not nailed anymore, of course, but there was no time to put it back on.
Giles states that the spell he cast here was his first casting. It will be revealed that this is not true. Whether this is a continuity issue or Giles is lying is unknown.
Driver Ed cars have a second brake pedal on the passenger side. As soon as Cordelia lost control of the car the teacher wold have stopped it.
When Catherine and Amy get switched back to their original selves, Catherine takes the fire axe that Amy is holding by using her powers. The wire used to pull the fire axe towards her as Amy holds it up and says "Mom! Please!" is visible.
When Cordelia is in the drivers ed car, there's a woman in the back seat all the way through the sequence.
Giles translates "the darkness breathes" in Latin as "tenebrae respiratis". That means "you, the darkness, are breathing". The correct Latin translation is "tenebrae respirant". ("Darkness" is singular in English and "tenebrae" is plural in Latin).