Audio problem: In the final song "Where Do We Go From Here", you can hear Spike still singing even after he has apparently stopped. He and Buffy continue singing until after the line 'When do the trumpets cheer'. It is noticeable because James Marsters sings the word 'cheer' slightly out of sync with everyone else.
Continuity mistake: When Buffy is being offered the 'doublemeat medley' burger by her boss, the burger looks different in close up than in the long shots. In the close shot, the burger looks overall bigger, more filling is visible and there is more lettuce sticking out.
Continuity mistake: Just before Buffy storms out on Spike, she puts on her denim jacket. When viewed from in front we can see the jacket is only half over her shoulders and her hair is loose. The shot cuts to view her from behind, and the jacket is now completely on and her hair is tucked under the collar.
Continuity mistake: The first shot of Maggie Walsh being impaled from behind with the skewer indicates that there is no one standing close by, judging by the amount of negative space around her. However, following shots reveal that the skewer is coming straight out of Adam's wrist, therefore he should have been visible in the previous shot.
Plot hole: In the flashback to Buffy in L.A., how did Angel get there with the front windshield of his car blacked out? Being a vampire, he obviously needs it during the day, but he also wouldn't be able to see traffic. And it just seems to be too much of hassle for him to remove it at sunset, just to reapply it at sunrise, just to remove it again, etc.
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Continuity mistake: In 'Graduation Day, Part 1' when Giles stabs the Mayor, as he takes the foil out of his chest you can see a wound on his shirt. When the shot changes it has disappeared. I know the Mayor is invincible and his wound heal in seconds, but it still takes a second or two for his wounds to close up, they don't just disappear.
Revealing mistake: The knives Giles throws during Buffy's training are a very poor CGI job if you watch it in slow mo. All three knives Giles takes off the wall are identical, with a broad curved blade and a plain black handle. The first one has a transparent blade as it flies toward Buffy, then we hear it bounce off the far wall and it's way out of scale for the distance. The second knife has a diamond-patterned grip instead of a plain one. The third knife conveniently spins in midair for a second so Buffy can kick it out of the way.
Other mistake: When we first see one of the Hellhounds at the clothes store that Cordelia works at, it jumps through the window, smashing the glass, and then attacks a customer who's wearing a tuxedo. But the Hellhound attacks the customer several seconds after it smashes through the window, giving the customer a chance to escape. But the customer just stands there unaware of the Hellhound, having not heard the window being smashed.
Continuity mistake: When Willow and Buffy are having breakfast, in the shot facing Willow she picks up her glass of orange juice and when the shot changes to Buffy picking up her coffee cup you can see the glass is still on the table and then Willow's hand reaching for it again.
Plot hole: After losing his soul, Angelus kills Jenny Calender's uncle, who is a descendant of the gypsy clan who cursed him. But, since there is nothing to suggest the uncle's room is in a public location, Angelus couldn't have gotten in the room without an invitation.
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Plot hole: In the 3rd time loop at the magic shop, the woman looking for the mummy hand looks surprised when Buffy knows what she wants. In the 2nd time loop, the woman tells Buffy that she called the shop 20 minutes earlier and was told that they had one. Therefore at least one of the shop's staff would be aware that a woman would be arriving looking for a mummy hand.