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".
Character mistake: Giles picks up the potential slayer Chao-Ahn from Shanghai in Episode 7.12, "Potential". However, when she arrives in Sunnydale (Episode 7.14, "First Date"), the language she speaks is neither Mandarin nor Shanghainese (the two main languages spoken in Shanghai), but Cantonese, which is not widely spoken there.