Visible crew/equipment: When Buffy, Willow, Xander and Giles all agree that Morgan is their one suspect, a camera and a cameraman can be seen in the reflection of the glass in the door labeled "Librarian", right after Buffy says, "Uh, priority check, Giles." A boom mic is also reflected in the top right of the glass when Buffy finishes her line with "talent show murder!" The mic can be seen throughout the rest of the scene from two different camera angles.
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). (00:08:30)
Other mistake: In the famous scene where Buffy tells Giles, "If the Apocalypse comes, beep me," she grabs her pager from out of shot. Trouble is, she's standing in the middle of her hall and there's nowhere she could have picked the gadget up from. (00:21:00)
Audio problem: When everyone is in the Bronze - just before the vamps show up - you hear the first line of a song being played, Ballad For Dead Friends by Dashboard Prophets, cut to outside and you see the vamps strolling along and killing the doorman, then cut back into the Bronze and the same line plays again. This is a total error in cutting the show, it is stated there is no live band but still the same line plays twice when that is not how the song goes.
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. (00:40:25)
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.