Continuity mistake: Buffy's birthdate starts at 1979. In "I Robot, You Jane", when the demon pulls up Buffy's file in the school system, it shows her year of birth as 1980 and her year as sophomore. But when her file comes up on the student's computer screen, it's changed to 1979 and that she is a senior. It wasn't until towards the end of season 1 in "Nightmares" that her birth year is 1981 (on her tombstone before she comes out as a vampire).
Continuity mistake: When Buffy is talking to Owen at the end, there is a woman wearing a red/black checkered jacket, sometimes carrying a red bag, walking up the stairs behind Owen several times. You can also see her behind Buffy in shots facing her.
Continuity mistake: When Willow hides under the table in the classroom after fleeing the pack, we see that it is on legs and doesn't touch the floor. Yet when Xander comes in and scans the room, he sees the table but Willow's feet aren't visible, even though they should be judging by the height of the table from the floor.
Continuity mistake: When Buffy finds Dr. Gregory's glasses on the lab floor she places them on the table, from the long shot she places them at the left end of the table near a plastic tub with a white lid, with the glasses open. Then it cuts to a close up where they are in front of a book on the right side of the table and are closed. Then cut back to the long shot and they are in the original place.
Continuity mistake: When Buffy leaves the Bronze (right before the Three attack her) to go home, she passes a strange-looking green-lit window. After the attack, she and Angel run past this window again, even though they're heading in the same direction Buffy was going anyway.
Continuity mistake: In the scene where we see Buffy's mum drop her off at school, when Buffy is worrying that her dad will not show up, we firstly see Joyce's seatbelt is on. We then see her again and it is still on. However after the shot goes back from Buffy to herself, we can see her seatbelt is off. Then when the shot comes back to her again it is back on.