Buffy and Willow are studying French and their notes are all over the table before they go to dance. However, when Xander runs in to collect a stake from Buffy's bag later, all the notes are gone.
At 35:40, both of Buffy's hands are seen holding the axe while the stabbing noise of the stake to the vampire is heard.
Buffy and Cordelia are talking about Joyce and Cordelia's arms switch from being crossed from the front view and against her hips when she is shown from behind and back again in every shot.
Spike refers to Angelus as being his sire. Later in Fool for Love (2000) it is made clear that Drusilla turned William (Spike) into a vampire. However, Angelus was the primary teacher of William, and these two formed a bond, so Spike feels that Angelus was his sire in this manner.
When Spike and his gang first break through the glass into the school, the stuntman filling in for James Marsters looks nothing like him.
As Spike walks down the school hallway (29:22 on the DVD), we see his reflection in a glass case to his left (the viewer's right).
EDIT: The glass case is on the viewer's left, and Spike's right. But even on zoom it's obvious it's only his shadow that is seen in the case.
At 21:28, as Buffy is cutting the cucumber with a machete, she never actually cuts all the way through it.
When Buffy and Spike are fighting in the school you can clearly see the person she's fighting, their hair is different from Spike's. Either it's a stunt double or James Marster's hair was in two different styles.
When Drusilla is first introduced she cuts Spike on his cheek using her fingernail leaving a trail of blood. The tube through which the blood comes out is visible.
Giles says that Spike is "barely 200," but later episodes indicate that he became a vampire in 1880. Based on his approximate age at that time, he would be closer to 150.
When Spike first sees Angel he called him Angelus but pronounces it as "Angeles" as in "Los Angeles". Considering they have known each other for hundreds of years, he would not make this mistake.