In filming there's a script supervisor concerned with continuity but only within that particular episode or movie and usually about details regarding clothes and hair and things like that. In a TV series I always think they should have a person who's job it is to oversee continuity for all the episodes, keeping all the details straight. This applies even to mundane shows as it helps keep things straight like if a parent is dead (MASH) and things like that. A show like BtVS which is creating its own world truly needed someone like that. Oh well I guess the creators either figured no one would notice or they themselves forgot.
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Shakatany