Visible crew/equipment: When Xander is in the bathroom after Buffy called him to look for the talisman, he bends down and grabs the talisman that lays under the sinks. As he stands the camera pans up to the mirrors and on the left side you can see the reflection of a crew member crouching over the hole to the old school. It's not the female manifest spirit as the clothes are wrong and she then appears from a different part of the room.
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Character mistake: When Buffy is looking around the new high school, encountering the first sign of the school being haunted, there is a notice board in one of the corridors entitled "theatre". This is the British spelling. Sunnydale is in America and therefore the word should be spelled "theater".