Factual error: After Buffy drags Xander down to the basement she locks the door and goes upstairs to find Dawn. When she locks the basement door, the handle is on the left side of the door and she turns the key to the right. In reality, a door with the handle on the left needs the key to be turned to the left to lock it. So Buffy did in fact unlock the door, not lock it.
Factual error: There is a short picture of a 17th century German newspaper. The actual text however not only is written in modern High German as opposed to Mid-High German, but also is full of errors (mixing female articles with male nouns is only one example). Funnily enough, Giles' incantation at the end of the episode is in correct German.
Factual error: When Giles and Cordelia are driving to save the girls from getting burned at the stake and are making the potion to make the demon show his true face Giles tells Cordelia to shred the Wolfsbane. This is a huge mistake as any Witch will know (my sister pointed this out to me) that Wolfsbane is highly poisonous and should never be touched with bare hands and Cordelia didn't have gloves or anything.
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Factual error: When Angelus is torturing Giles in this episode he is seen with Giles' glasses, and he cleans them by breathing on the glass and wiping with a cloth. Vampires don't have breath, as Angel tells Xander in 'Prophecy Girl' from season one - even if he can force some air out of his body, it wouldn't be warm, moist air, which is needed for condensation to clean glasses with.