Continuity mistake: The scene where Xander is on his skateboard, he becomes distracted seeing Buffy walk up the stairs and accidentally hits the pole. When the camera pans back, you can see Buffy is out of view, and is nowhere to be seen. Because she was still at the top of the stairs when Xander hit the pole, you should have been able to see her walking in the background.
Continuity mistake: When Cordelia is giving her May Queen speech, Willow notices 2 body guards standing around. In both shots you can see the same 2 girls, wearing light blue and grey, walk behind The Body guards. The same girl in light blue can also be seen in several different shots, in the crowd listening to Cordelia and walking around as Buffy talks to Willow and Xander.
Continuity mistake: A cut scene shows the sun had just gone down right before Buffy heads to the Bronze and Joyce tells Buffy she will make them dinner if she chooses to come downstairs. This would assume it is evening. When Buffy kills Luke she says sunrise is in 9 hours. Considering this episode takes place in March, that would mean the sun would have gone down around 7pm. But 9 hours from sunrise would be around 10pm.
Continuity mistake: When Buffy is shown pulling the secret chest out of her closet with weapons against the vampires, the window behind her shows daylight, but when she steps out of her window it is fully dark. There is also a cut scene right before that shows it was twilight, but there was late afternoon sunlight shining through the windows of her room. It's not possible for the sun to go down that fast.
Continuity mistake: Buffy's history teacher is not the same person from episode 1 or 9, originally a woman, the teacher is now a man. Cordelia also notes Buffy doesn't know where the class is due to ditching, but we saw Buffy in her history class with Cordelia in The Puppet Show. How could Buffy not know where her class is only 1-2 weeks later?