Continuity mistake: When the detective is interviewing the woman in the alley, he mentions that the murder took place "last night". In "Bad Girls", we see Buffy visiting Faith the day after the murder, and that night is presumably when she has the dream about drowning, so by the time the detective is asking this question it is actually two nights after the murder, not one.
Other mistake: When the detective is interviewing the woman in the alley he says "So you heard the man scream about what time?", but Finch didn't scream as he died.
Continuity mistake: Willow's hair changes position between shots when the vampire brushes her hair back and kisses her.
Continuity mistake: Whenever we see the two Willows together in this episode we see that Vampire Willow is understandably very pale in comparison to the living Willow. However, in the library with Cordelia, when Vampire Willow says 'How about dinner?' her face is no longer pale.
Other mistake: In "Doppelgangland", Vampire Willow struggles to remember Cordelia's name. However, it is still Willow, she knew Cordelia from being human (we see this in The Wish as well).
Revealing mistake: Near the end when the good Willow says goodbye to the evil Willow and hugs her, there is a shot of the back of the good Willow's head and the evil Willow's face. You can tell that the good Willow is a body double wearing a wig - there's something circular near her scalp, possibly an elastic band.
Revealing mistake: Right at the beginning of the episode, Buffy is sat outside with Willow and Willow is levitating a pencil. The pencil is obviously CGI as it stands out from the rest of the picture and doesn't cast a shadow. It also disappears from view whenever there is a side-angle shot of Willow.
Revealing mistake: Both the good and evil Willows' faces are barely seen onscreen at the same time due to them being played by the same actress, but when they occasionally are the good Willow stands out from the picture more than the evil Willow. She must have been filmed separately from the good Willow and edited in later.
Revealing mistake: When evil Willow licks good Willow's neck the neck that you see is a lot longer than either of theirs. Since both Willows' faces cannot be filmed at the same time a body double must have been used for this shot.
Audio problem: While Faith is stabbing the demon in his apartment, we hear the sound of her knife going through, and him yelling in pain. However, the last sound of her stabbing him comes a little late: The knife isn't even touching him.
Revealing mistake: After Faith brings Angelus back, when she goes to punch him and he blocks, the stuntman switch is very obvious - he's noticeably taller, has different hair and doesn't even seem to be wearing any vampire make-up.
Revealing mistake: In the scene where Buffy is fighting the big scary lunch lady, look closely in the far away shots because you can see that the big lunch lady is now a skinny little stunt double. (00:41:55)
Continuity mistake: The time on the clock, when Buffy spots Jonathan, changes dramatically between shots.
Continuity mistake: When Willow hands Giles the pages she stole from the books of ascension, initially the folded side faces to the left, with loose edges of pages to the right, then in the next shot the folded edge is now on the right. (00:36:25)
Continuity mistake: After Buffy slams the Gavrok spider thing on the ground with her back, she gets pulled up by Angel. We see this shot from the back, and we see that the Gavrok is no longer on the floor or on her jacket. In the very next shot, we see Angel kick it across the floor. Where did it come from?
Answer: She has superpowers, ergo fast movement. The reason she outruns him so easily in "Touched" is that she stops trying to actually fight him and just dodges instead.
Shay